Sunnie was on Denamarin for about a year for elevated levels of unknown source...she's been fine ever since (that was 4 - 5 years ago if I remember correctly). I hadn't noticed any increase in drinking but Sunnie's not a big drinker so perhaps she just seemed more like a normal dog and it escaped my attention. I know we had no leakage.
I'd talk to the vet, though...excessive drinking and urination issues can themselves be a symptom of liver disease.