There's a Catullus poem that suggested they did, but clearly it wasn't all Romans, and some of the others even derided them for it.
(I briefly tried to figure out how to promote that, but I know nothing about starting campaigns of that sort. shrug)
if you want to kill them that is. Pee need to be diluted with water before being used as a fertilizer.
Furthermore, the idea I had was not that urine would be the only fluid the tree would get, but that peeing on a tree would mean flushing the toilet one less time per day. Most toilets use premium tap water, not grey water, and water shortages have been a big global issue.
Plus tree were dying from drought in California by the millions when I had the idea. I'm sure peeing on them would have been less deadly for most of them than extreme drought.
It was summer but no drought though. I guess it depends on the trees.