Yes but it's a share of the eventual block reward. If fees (bribes) are collected out-of-band, they are not included in the block reward, thus not likely distributed to hashers.
Discussion
It's so not.
The majority of pools these days pay a low fixed rate for hash regardless of their success mining blocks or the fees contained in the blocks.
Again: most pool payouts have nothing to do with blocks or fees these days.
Out of band payments (and block luck and fees) MIGHT EVENTUALLY help pools stay solvent and provide a higher fixed hash price to their miners, but there is no relationship between them in most pools now)