Do the gods hear petitionary prayer?
Well, let's take one example. Does Earth hear petitionary prayer?
Different people would give you different answers to this question. Speaking for myself, while it would be easy to say no, that's not quite right.
Here's what I would say. Whether or not Earth qua planet hears our petitionary prayer, we don't know. Here's what we do know: Insofar as we ourselves are Earth and of Earth, Earth does indeed hear our prayers.
In some ways, the entire question strikes me as wrong-headed. We all have work, including the gods. Why would we think that answering our prayers is among the work of the gods? The gods, in fact, are already doing their sacred work all around us every day: the Sun shines, the Storm gives rain, the Earth brings forth. If you ask me, it's not their job to make sure that—to quote Quentin Crisp—I get that blue bicycle that I always wanted.
When it comes to the big things—life, food, health—those are the gifts of the gods. (Or not.)
As for the other things—blue bicycles, for example—I think that it's up to us to take care of those things for ourselves and, most importantly, for one another.
That, I believe, is why They gave us the Tribe.