If you're accurate enough not to pee on the counter then the only thing holding back someone so inclined is the social taboo. It's not like the kitchen sink where stuff regularly goes in there. Does pee harm pipes? Will it make the sink bowl radiate a permanent smell? I just hate wasting water by flushing only pee but also don't like letting pee sit for an excessively long time.
Oh my sink is far too small to wash anything beyond hands. I wash my face in the shower or with a rag.