I don't see this as likely. Global warming is not an extinction level event (for humans! for a lot of other life, it will be, although habitat loss may well play a larger role in that.)

My own speculation on the Great Filter is that any intelligent alien civilization is almost certainly a race of social predators that evolved - and thus are in competition for resources.

I worry that competition between individuals and individual states necessarily ends in the destruction of the environment on which they depend and quite likely in direct destruction in war with advanced technology.

Us humans need to find some other paradigm under which to move forward, capitalism and competition, which have brought us such amazing results to date could well also be our undoing.