When you ask would it have been on their minds, what do you mean?

Were the Iliad and Odyssey poems that the majority would have known? Most definitely.

Would that have been an inspiration to form their own leagues? Quite possibly. The idea of success by grouping together could have stemmed from the combination of Greek states within the Iliad but there is also the chance that they may have just realised they have similar interests and could work well together.

Hm, you mean the founders of the amphictyony? Using the Trojan War myth as a paradigm for an alliance of states? Well, it's not impossible, but that period is so shrouded in a lack of evidence that it's not really possible to say.

That's really the upshot of this answer: insufficient data.

I know of one argument that would suggest the contrary: that the idea of multi-state alliances only really arose with the Persian Wars, and that was one of the reasons that Homer became so popular at that time. (I'll dig up the reference if you like.) It doesn't really stick: we don't have evidence of Homer's popularity prior to the late 6th century, but we do have clear evidence of the popularity of the Trojan War myth. But the fact that someone can seriously suggest that should serve to illustrate that, prior to 490 BCE, an awful lot of specifics in Greek history have only a very shaky grounding in evidence.

I'm not sure what you mean about traditional dates, by the way. Is there a traditional date for the founding of the amphictyony? I can't find any ancient evidence on its founding, beyond Aischines' statement about which states were the founding ones. Or are you thinking of the First Sacred War which may or may not have occurred in the early 6th century? Homer didn't really have a traditional date either: he has a traditional date now ("ca. 730 BCE" is the usual sound-bite, and it's wrong), but there's no very strong agreement between ancient sources on a traditional date.