I mean, not really. The Romans, as always, picked and chose the parts they liked and integrated them into their own mythology. The Roman pantheon was a superset of the Greek pantheon (among others), as evocatio was used as a final part of conquest. The Romans also stole the gods of their foes, and more than just the Greeks.
Roman culture, though, was heavily focused on superstition and virtue, rather than logic, and is not in any way a retread of Greek culture.
Republican Romans would have lynched you for calling them "Greek". Romans were well aware of their Archaic history and there was very much a sense of Greeks being overly pompous, fanciful, dissolute foreigners, albeit somewhat related.
The spurts of Greek (and later Persian and Egyptian) fashion in Rome existed precisely because they found it exotic. Otherwise Roman and Greek myths link at several levels purely and simply because they shared the same root. Romans didn't really "snatch" Gods from Greece, they were already theirs. And they "enriched" their existing archetypes with new attributes from outside as the Empire grew to pacify the subjugated peoples.
