Er, sort of. Gay as an identity is a very recent thing; Achilles would not have identified as a gay man. And that he had an eromenos, Patroclus, does not necessarily make him gay as we understand it. And whether they had an actual sexual relationship is also debated; whether their relationship was pederastic or romantic further so.
It would be incorrect to apply contemporary understandings within our culture to a relationship within a completely different context.