Did contemporary scholars draw a connection between Great Schism and Crab Nebula Supernova (1054 A.D.)?

There are several points to be considered in this question. Let us start by seeing some hard facts. As quoted by Wikipedia article SN1054:

"Crab Nebula probably appeared in April or early May, rising to its maximum brightness of between apparent magnitude −7 and −4.5 (brighter than everything in the night sky except the Moon) by July. The supernova was visible to the naked eye for about two years after its first observation. Thanks to the recorded observations of Far Eastern and Middle Eastern astronomers of 1054, Crab Nebula became the first astronomical object recognized as being connected to a supernova explosion."

Mayall, Nicholas Ulrich (1939). "The Crab Nebula, a Probable Supernova". Astronomical Society of the Pacific Leaflets 3 (119): 145.

The important facts are the months in which each phase of the supernova took place. Supernovas have a characteristic curve (actually, two or more types of curves) which describes how light emission takes place. From a low initial value (April/May in the case of SN 1054), emission increases rapidly to a maximum within about 20-40 days (July 10th), then decreases more slowly over a period of 40-60 days.

Now, the position of the supernova in the sky is also relevant. In this case right ascension is 5h34m, declination is 22 degrees. However, in early July (such as now), the sun is very close to this position, at least during daylight hours as seen from Northern Europe. Please consider the following screenshot from the Stellarium software, calculated for Paris on July 13, 2015.

Basically, what can be seen here is that the 1054 Crab Nebula supernova is at about 20 degrees removed from the sun during daylight hours, when at maximum emission. It must have been difficult to see in this conjunction, as are the planets Mercury and Venus when very close to the Sun. Difficult - but not impossible. Moreover, this difficulty would have been precisely the same, seen either from North-Western Europe or from East Asia. At earlier or later dates, the Sun would have been further apart from the supernova thus lessening glare, but the supernova's own emission levels were much lower.

Now, consider where the supernova has been documented from: very clearly in China and Japan, with perhaps one observation from the Middle East. Does this mean it was not observed in Europe? One must think not, even though local conditions could have interfered: increased cloud cover or volcanic emissions. These could have had an influence in some parts of Europe, but not on a sufficient scale to affect the complete continent[2].

Thus, we are confronted by a natural phenomenon that, from a physical standpoint, could very well have been observed from Europe as from Asia, but that has been clearly documented only in the East.

To my mind, this is already a significant development, leading us to a series of questions:

1. Was the supernova detected in Europe, but not reported? If so, detected by whom? Why was is not reported? Or if reported, why has the information not been conserved until now?
2. Was the supernova not detected in Europe, and if so why not? Was there less interest in celestial phenomena than in the Orient? Or was there less knowledge available to interpret observed phenomena?
3. Why is there no report of observations of the supernova in the Western arab word, either the Magreb or the Andalous? These civilizations were perfectly up to date on scientific advances, and well connected with the rest of the arab-speaking sphere of influence (e.g. Baghdad).

Perhaps we need more hard information in order to give correct support to a serious explanation of the facts. In the present state of our knowledge, I am afraid we simply cannot give a definite answer to the question.

[2] Compare with the 1783/84 Laki event, that affected mostly the British Isles and parts of the North of France - but not Southern Europe or the Balkans. This is typical of wind patterns over the North Atlantic.