If your peonies have been in the ground for a few years I don't think it'll make any difference at all. Maybe on 1st year peonies allowed to bloom but not on established.

I have to agree with lizbest that it makes no difference once the peonies are established. You may find some seedlings but those can be removed. Although I no longer use them the dried seedheads make interesting additions to flower arrangements and baskets of dried flowers.

I don't think it makes much difference once established.

I always deadhead the seed pods that I can easily reach, and leave the few that I can't be bothered to wade in and get. I don't like the looks of the seedpods, and they can be prominent on their long stem sticking out from the rest of the shrub.