As usual when this topic comes up, people are coming at it from at least 3 different directions, so you are getting different/conflicting answers.
"Round balls" can be used in at least 3 different kinds of guns: Rifles, as patched round ball, revolvers, or smoothbores.
Generally speaking, for PRB and revolvers you want pure lead. However, as was said above, people will sometimes put a pea-sized piece of tin in their pot, and this will not appreciably change hardness but can considerably improve mold fillout. I find you can avoid the tin and get good fill by just running a bit hotter, usually. But I have never had a problem with mold fillout in a round ball mold regardless.
For smoothbores, they don't really care about hardness. I shoot "wheelweight" lead for my roundballs in my smoothbore musket. However, the ball diameter will change using alloy vs. pure lead.
But to answer your question directly, adding tin will increase hardness, depending on how much you add, and generally improve mold fillout.