No, I think we are their cultural and spiritual heirs but probably not in blood to any great extent, other than the common Indo-European ancestry all Westerners share. The Roman Empire stands between us and them, so that there probably was some inevitable mixing around of families that occurred as a result of the extent of the Pax Romana -- and the resulting import and export of Greek slaves here, there and everywhere. The Romans knew their cultural superiors when they saw 'em!
The Celts were already pretty much in place and making characteristic artifacts while the Myceneans were just getting started with their citadels . . . and of course that LONG predates Homer as well as the Greeks Homer was singing about.
I often wondered if the remaining Trojans might have been the origin of the Phillistines or sea people who simply fled down the coast as refugees.