It counts, because it was still pee. :)
Also, that doesn't cover all pee from all animals from the first pee of the first thing to have a bladder till now.
True, but due to time present, pee volume per animal, the dinosaurs really make up the bulk of the total. The biomass pre-Dino was relatively small in comparison, and post Dino was a relatively limited timeframe. Remember, there is as much time between a T.rex and a stegosaur as there is from a T.rex to now.
But yes, w.r.t. Drinking water that was once pee, if Dino pee counts, then, yes.