On current evidence, no, not so far as we can tell. I'd better disabuse you of a couple of misconceptions you've got here:

1. Troy did not fall at the time you're thinking of. It was inhabited continuously until ca. 950 BCE, and there's strong cultural continuity between the archaeological phases up to the start of at least Troy VIIb2 (ca. 1150). Troy VIIa and VIIb1 should really be regarded as late phases of Troy VI (VIi and perhaps VIj).

2. Troy was never a major trade centre. Evidence is thin on the ground, but the clearest sign we've got is that very nearly all of the pottery that's been found from Late Bronze Age Troy is Anatolian ware. Troy had no decent harbour (there was an inlet by the city in ca. 1200 BCE, which has since silted up; but it was shallow water). There was some trade across the sea, but not on a large scale. Troy at that time was comparable in size to some other Anatolian centres, but documentary evidence tends to suggest that the politically and economically important parts of western Anatolia were further south, in central Asia Minor. That doesn't necessarily translate into trade, of course, but as I said, evidence is sparse. In later centuries, Byzantium was where it was all happening. Troy never really seems to have had the potential for the kind of stranglehold on the Hellespont that you're thinking of.

That said, the archaeology of Troy's citadel certainly looks like the city was burned ca. 1190-1180 (ending the Troy VIIa/VIi phase), and there was structural damage to the stonework on the citadel ca. 1270 (probably associated with the end of the Troy VIh phase).

The later of these incidents (the end of Troy VIIa/VIi) is most simply explained as part of a wide-ranging wave of destruction and/or abandonment across Greece, Anatolia, and the Levant, all within a few decades after 1200 (and yes, 1177 is a pretty good end-date for this wave). This is the so-called "Bronze Age collapse", and the reasons for it are not at all clear, but are almost certainly caused by a combination of multiple factors. Many cities in Greece were destroyed, and others in Anatolia were abandoned or destroyed at this time. Troy was not one of them; but the fire in Troy VIIa/VIi certainly invites us to think of it as related somehow.

The earlier incident (the end of Troy VIh) is the one that is nowadays most usually connected to a hypothetical "Trojan War". This is for several reasons: the greater wealth of Troy at that time; documentary evidence of political upheaval in Troy, and of Troy's significance in international relations across the Aegean; and the fact that at the later date, ca. 1190-1180, the Greeks were much too busy worrying about their own civilisation coming to an end to think of attacking a city which was firmly within the Anatolian cultural sphere, which was no longer especially significant, and which belonged to an empire that was also falling apart, all at the same time.

Many cities in the north-eastern Mediterranean were abandoned or destroyed in the early decades of the 1100s (Mycenae, Gla, Pylos, Hattusa, Cyprus, Ugarit); many more suffered severe damage but survived in reasonable health (Thebes, Knossos, Troy), some had their downturns quite a lot later and so shouldn't be linked to the collapse (Miletos), and others show no signs of any downturn (Ephesos). Picking Troy from this list as the ultimate cause of the collapse would just be arbitrary favouritism.