It does. The way pros hit, string tension drops considerably in only a few games, and the same applies to the air pressure inside the ball as well as the amount of felt on its surface. New balls tend to fly faster and longer, so a tighter stringbed is required to maintain the same level of control.
New balls also have more felt, which should make it somewhat easier to impart spin on the ball. Now whether higher tension means more spin is, I think, open to debate, but I believe convetional wisdom has it that the answer is positive.