Was Yahweh a god in a possible Edomite Pantheon?

Short answer: yes.

The earliest evidence for Yahweh worship is sparse, especially regarding its precise 'nature'. For the very early Edomite religious concepts it is even scarcer. For Yahweh it is also – sometimes fiercely – contested in many details. Not in the least because most devout deny any development in these concepts, taking the scriptures as inspired, first and final words on these matters.
_{– Bob Becking, Lester L. Grabbe (eds): "Between Evidence and Ideology: Essays on the History of Ancient Israel read at the Joint Meeting of the Society for Old Testament Study and the Oud Testamentisch Werkgezelschap Lincoln, July 2009", Oudtestamentische Studiën, Old Testament Studies, Brill: Leiden, Boston, 2010)}

A very similar effect is seen for more secular scholars who tend to early-date many events or trends. One such thing is most probably the undeniable trend towards monotheism as "until finally consolidated as the sole form of Israelite religion in Babylonian captivity." This is much too early in this 'definity' (sic).
_{(But not the main point of this question… A glimpse of this discussion to be found in "Monotheism, what monotheism"-Bob Becking in: Bob Becking, Meindert Dijkstra, Marjo C. A. Korpel, Karel J.H. Vriezen (eds.): "Only One God? Monotheism in Ancient Israel and the Veneration of the Goddess Asherah", Biblical Seminar 77, Sheffield Academic Press: Sheffield, 2002)}

It remains a problem that from our main textual evidence we have not that much to go on for Yahweh himself:

The origin of Yahweh worship is hidden in the dark prehistory of the people of Israel. The tradition in Ex 3 mentions Sinai / Horeb as the starting point for the worship of Yahweh, but it is not clear whether this tradition is historically correct. The lack of data makes it impossible to make more than one assumption. In my opinion Yahweh was the god of an immigrant group from the southern East Bank. In the Iron Age, his worship was linked to the worship of both the Canaanite god El / ilu and the god of the "Exodus" group. The Old Testament texts are all of later origin, and therefore it is a tour de force based on literary-critical decisions to describe the origin and original character of the deity Yahweh without falling into a circular argument.
_{— Bob Becking: "Jahwe", Wibilex, 2006}

For Yahweh at Edom we have nonetheless some basic facts to observe:

The absence of references to a Syrian or Palestinian cult of Yahweh outside Israel suggests that the god does not belong to the traditional circle of West Semitic deities. The origins of his veneration must be sought for elsewhere.
A number of texts suggest that Yahweh was worshipped in southern Edom and Midian before his cult spread to Palestine.

By the 14th century BCE, before the cult of Yahweh had reached Israel, groups of Edomite and Midianite nomads worshipped Yahweh as their god. These data converge with northern traditions, found in a number of ancient theophany texts, according to which Yahweh came from Edom and Seir (Judg 5:4; note the correction in Ps 68:8)) […listing place names as evidence for a toponymic origin of the name 'Yahweh'…] All of these places — Seir, Mt Paran, Teman and Sinai – are in or near Edom.
_{— Karel van der Toorn: "Yahweh"; in: Karel Van Der Toorn, Bob Becking, Pieter W. Van Der Horst (eds): "Dictionary of Deities and Demons in the Bible", Brill: Leiden, Boston, ²1999.}

The Edomite national god Qaus/Qos is at least as closely related in origins and syncretistic development as El and Yahweh. But that is my personal conclusion. A more recent discussion of this problem concludes:

[…] we have reviewed the primary material and textual evidence for the veneration of Qos among the inhabitants of ancient Edom (and to some extent, their successors, the Idumeans and Nabateans). We have considered what some scholars have posited about the nature of Qos, theories that are based largely, though not exclusively, on what is known of the desert dwelling deities of the Syro-Palestinian milieu. Finally we looked at some of the theories surrounding the enigmatic connection between Yahweh and the god of Edom, concluding that Yahweh and Qos both originated in the south, were worshipped together as deity and divine symbol, and through various circumstances, ended up becoming the respective deities of Judah and Edom due largely to the political circumstances of these respective groups.

Despite the case that I have attempted to make for the worship of Yahweh/ Qos, the presumed relationship between these two important deities will likely remain shrouded in mystery, as will many things pertaining to ancient Edom and the tribal coalitions of the Negev and northwestern Arabian Peninsula. We simply lack the kind of material and textual data necessary to make any solid conclusions. nevertheless, as Blenkinsopp points out,

“in a sense, all our knowledge of the past is hypothetical and probabilistic, and the task of the historian is always that of coming up with a better hypothesis.”

That being said, it has been my task to take into account the relevant biblical and extrabiblical data at hand and to work toward a new, provisional interpretation by which to understand the relationship between Yahweh and Qos. For it does seem to be the case that a connection between Yahweh and Qos would have existed, given the glimpses in the biblical text of Yahweh’s southern origin and the relationship between Judah and Edom as perceived by the biblical authors. It is, therefore, my hope that the hypothesis set forth in this analysis will contribute to a better understanding of the nature of the relationship between these two unique and enigmatic deities of the ancient near East.
_{— Justin Kelly: "Toward a new synthesis of the god of Edom and Yahweh", Antiguo Oriente: Cuadernos del Centro de Estudios de Historia del Antiguo Oriente Vol. 7, 2009. (PDF)}

One interesting thing relating back to the post-exilic data in forming Israel identity is that the close relationship, a 'brotherhood', with Edomites is that after the Exile this boundary was apparently deepened. Yahweh coming from the Edomites did not help as much as the status between siblings soured:

By presenting the ‘other’ in dark colours, a boundary is drawn between ‘we’ and ‘they’. In the period after the exile, the Edomites still were seen as related as well as inimical. The tradition on the betrayal of Edom functioned as a boundary marker of the community. ‘We’ were thus separated from ‘they’. ‘We’ – Israel – were as a result of the divine grace returned from exile. ‘They’ – the Edomites – were excluded as badly behaving brothers. In order to construe this divide a claimed tradition was constructed.
_{— Bob Becking: "The betrayal of Edom: Remarks on a claimed tradition", HTS Teologiese Studies/Theological Studies, 72(4), a3286, 2016.}