Can brownie dough sit?
If the flour is self-rising flour, then it shouldn't be allowed to sit for too long. However, this wouldn't result in it being "impossible to pour" - it would just prevent the item(s) from rising properly when baked.

If I had to guess, I would point to the chocolate as the culprit. If your batter/dough recipe uses melted chocolate (as opposed to just cocoa powder) then it is almost certainly going to solidify again as it cools. In which case, you can simply heat it again (gently - you don't want cook the eggs!) to loosen it up a little before pouring it.