Most likely, you probably would. I have a friend who had an unneutered male cat and he sprayed all over, even though he was the only cat in the house. Their urine also smells stronger as well, just in the litterbox, even if he's not actively spraying.
He stayed at my house for just three days, and by the third day the smell of spray was just overwhelming.
Plus, there's the caterwauling and trying to escape to mate, not to mention you are putting your little friend at risk for testicular cancer.
I really suggest you get him neutered - the two of you will be much happier if you do.