Not really.

The frequent replacement of sperms cells is “helpful” in a sense to reduce the incidence of chromosome abnormalities like Down syndrome. For women, since they are born with all the eggs in their body, those eggs age with them and with that age it is thought that the chromosomes get kind of “sticky” and can have trouble dividing easily. This is why Down syndrome can be seen more frequently with older moms.

The same is not true to sperm. However, there are risks associated with advanced paternal age and those risks are associate with mutations. For example order dads have a high chance of having a kid with achondroplasia. This is thought to be related to the fact that the sperm of an older man has undergone more cell division leading to more chance of these small mutations.