positive shows of support vs excessive negativity, criticism, empty seats etc - both on game day and the rest of the week - impact team performance?"

My answer, yes, absolutely. Do I think it could take a mediocre program like BYU and inspire it to win over a Big Boy like Georgia? No way.

Having said that, 95-99% of winning comes from the Coaches and Players preparation before a single fan plops his/her behind down in the stands.