I neutered my rescue at 2, and at 3.5 years he is still marking exactly where my female goes. He also is very particular about his pooping habits, and, no, he won't go on a leash, he has to have his "space."
On the flip side, one of my rescues came to use freshly neutered, he was about 5 or 6, and he totally gave up all his testosterone-driven bathroom habits, went anywhere, on leash, off leash, didn't matter to him. And he never had an accident in the house, bless his heart, my Rosco.
I wonder whether it matters that Orick, my current boy, is straight Czech bloodlines with all the drive, and Rosco was ASL and pretty mellow. Hmmm.