Was the interior of Hagia Sophia in Constantinople ever covered with mosaic icons?

It was a very richly decorated building. I would say: it still is. Architectural simulations of the kind depicted in the question are obviously far from complete. But the complete lack of images, while the ornaments were taken into account, might also indicate an (idealised?) Muslim stage of the structure as the goal.

But the rendering is very likely just incomplete, because even today not only are some of the icons visible but also the ornaments that did survive were not taken into account in that simulation:

Dual-coloured vines in the soffit of the north-eastern exedra arcades of Hagia Sophia at gallery level (possibly sixth century).

It depends a bit on how this "once" is defined. The building originates from the 6th century ("537 A.D- The reconstruction was completed with the lavish decorations and ornaments") and was therefore subject to changes, additions, removals, over plastering, reconstructions over more than a thousand years. Even under Byzantine rulers unchallenged from outside, either by Christians or Muslims, the appearance was altered from "the original".

The church was richly decorated with mosaics throughout the centuries. They either depicted the Virgin Mother, Jesus, saints, or emperors and empresses. Other parts were decorated in a purely decorative style with geometric patterns. The mosaics however for their most part date after the end of the Byzantine Iconoclasm of 800 AD.

Originally the nave was lined with intricate Byzantine mosaics which portrayed scenes and people from the Gospels. After the Ottoman Conquest, many of these mosaics were covered over with Islamic calligraphy and only rediscovered in the 20th century CE after the secularization of Turkey (Hagia Sophia became a museum in 1935 CE). This includes the mosaic on the main dome which was probably a Christ Pantocrator (All-Powerful) which spanned the whole ceiling and is now covered by remarkable gold calligraphy. On the floor of the nave there is the Omphalion (navel of the earth), a large circular marble slab which is where the Roman and Byzantine Emperors were coronated. One of the final additions the Ottoman Sultans made to finalize the transition from Christian basilica to Islamic mosque was the inclusion of eight massive medallions hung on columns in the nave which have Arabic calligraphy inscribed upon them with the names of Allah, the Prophet, the first four Caliphs, and the Prophet’s two grandsons. The Ottomans also added a mihrab, a minbar, and four enormous minarets in order to complete the transition to a mosque. (Source: Hagia Sophia)

One old description emphasising an important aspect – also of interior decoration – of how it looked is found in Prokop:

Procopius: De Aedificis:
The church is singularly full of light and sunshine; you would declare that the place is not lighted by the sun from without, but that the rays are produced within itself, such an abundance of light is poured into this church… Now above the arches is raised a circular building of a curved form through which the light of day first shines; for the building, which I imagine overtops the whole country, has small openings left on purpose, so that the places where these intervals occur may serve for the light to come through. It is further complicated by what is meant with "covered in mosaic icons". Some of the mosaics are lost, some of them are buried under newer layers or destroyed. Some of those were or could be recovered. Either in their physical form or at least as drawings. But not all of the decoration were icons.

One example of a reconstructive drawing of such an icon:

Fossati drawing of the emperor John V Palaeologus in the eastern arch, north side The mosaic of this emperor, who ruled from 1341 to 1391, has only recently been uncovered. It dates to ca. 1354. From Natalia B. Teteriatnikov: "Mosaics of Hagia Sophia, I anbul: The Fossati Restoration and the Work of the Byzantine Institute", Dumbarton Oaks Research Library and Collection: Washington, 1998.

And a physical panel:

The panel of St. Ignatios Theophoros was discovered by the Byzantine Institute in 1935 and dates to the end of the ninth century. It is located in the third lunette from the east in the north tympanum. St. Ignatios, a bishop of Antioch (martyred during the reign of Trajan [78-117]), is shown with short hair and long beard. His name is inscribed vertically on both sides of his figure. He wears a white sticharion, white phelonion, and an omophorion decorated with crosses made of two stripes of purple and blue tesserae. His right hand is raised in a gesture of blessing, and with his left he clasps a Gospel Book. Placed against a gold background, he stands on a dark blue ground between two diamonds with circle insets. (source: Teteriatnikov)

The building was not covered in mosaic icons like a collage of comic strips, but very heavily decorated, with indeed *many *icons. Out of all those mosaics used, most were ornamental and intended as a "play with light".

Despite the considerable transformation and loss of much of the sixth-century mosaics, particularly in the galleries, it is possible to reconstruct tentatively the overall design of the original mosaics of Hagia Sophia.

The mosaics are either completely lost due to numerous earthquakes, structural repairs and additions, or they have simply been changed to accommodate the needs or aesthetic tastes over a period of almost 1500 years. During Hagia Sophia’s use as a mosque, the mosaics were gradually concealed with paint or plaster and a considerable fraction has still not been uncovered to this day (e.g. Plate 15). On the basis of the sparse archaeological findings and the drawings and watercolours by Cornelius Loos (around 1710) and the Fossati brothers (1847–1849), Karen Boston has a empted a reconstruction of the original mosaic decoration of Hagia Sophia. See Karen A. Boston, ‘Imaging the Logos: Display and Discourse in Justinian’s Hagia Sophia’ (PhD, University of London, 1999), 175–217.

Most of the ornamental mosaics at ground level are believed to date to the sixth century. Here, glass mosaics cover the entire ceiling of the inner narthex, including the window so ts on the west and the lune es on the east as well as the aisles. These mosaics consist of geometric patterns and crosses on gold ground. Typically, ornamental borders outline the individual architectonic surface units. In the narthex, the border is composed of interlocked dark blue and silver stepped patterns, decorated with red and green jewels (Plates 8–11), while in the aisles it is a band of interlocked red and gold stepped designs, flanking a sequence of alternating swastikas and quatrefoils that are inscribed into dark blue squares and roundels, respectively (Plates 12, 13). These ornamental borders enclose a large double cross in the apex of the vaults. The surface units between these decorative borders can basically be considered the picture spaces and are decorated with a limited repertoire of geometric shapes, stars and Latin crosses with jewelled cross arms. One motif that prevails in the groined vaults of both the narthex and the aisles are pointy multicoloured egg-shaped designs that have been identified as lotus buds or winged palmettes (Plates 10, 11, 14). Other conspicuous elements are huge jewelled Latin crosses in the barrel vaults of the aisles (Plates 16, 17) and two continuous braided large-angled zigzag bands in the intrados of the transverse arches (Plates 12, 29). These bands are interwoven so as to form a chain of rhombi and their cross points are interlaced by circles, creating together an endless string of knots. The tunnel vaults in the passageways that pierce the western subsidiary piers and the southern bu ress piers are h*m*geneously covered in different carpet-like patterns of grids, diamonds, quatrefoils, squares and roundels on a gold or silver background (Plates 18, 19). The principal colours of what are believed to be the original sixth-century mosaics were gold, silver, red, blue and green.

The lack of monumental figurative mosaics in the sixth-century design of Hagia Sophia has led to speculations about the underlying reasons. It has been suggested that the large scale of the building is not conducive to figural representations or, in fact, that time was too short to allow for a more elaborate decorative scheme. However, I do not believe that the mosaic decoration was a choice of compromise. Rather, the visual effect of the ornamental mosaics provides at least part of the answer. The original design of the ground-floor mosaic displays an astonishing consistency in its repertoire, creating a unity that served as a vehicle of light rather than providing any exclusive visual focus. Procopius explicitly refers to the non-existence of a specific focal point, which indicates that his description and the mosaic decoration both reflect and share an aesthetic of an all-encompassing visual experience.

From Nadine Schibille: "Hagia Sophia and the Byzantine Aesthetic Experience", Ashgate: Farnham, Burlington, Farnham, 2014.

So yes, the Hagia Sophia was once covered with mosaics, and that enormous building had many more mosaic icons than visible today. But it was not covered in mosaic icons as practically the only means of decoration.

How did this look like what is now lost not or not yet uncovered or recovered? Impossible to know with certainty. But quite easily imagined if we look at the evidence found in other churches of that period and style when compared to the extent mosaics in the Hagia Sophia:

In San Vitale: Lunette on the northern presbytery wall showing Abraham feeding the three men/angels and the sacrifice of Isaac.
And in the Hagia Sophia:
Detail, Deesis, head of Christ
This image reveals a refined realistic manner of execu- tion. The facial features are strongly delineated. There is a soft, almost sculptural modeling of all the features. The mosaicist was able to achieve a painterly quality through the use of detailed underpaint and miniature tesserae, especially in creating the skin tones.

And this can be detailed even further by looking at the physical properties of the materials employed at the time. Done so surrounding Ch. 6: A Quest for Wisdom: The 6th-century Mosaics of Hagia Sophia and Late Antique Aesthetics; in : Chris Entwistle and Liz James (Eds): "New Light on Old Glass: Recent Research on Byzantine Mosaics and Glass", British Museum: London, 2013.