You can grow peony plants from seeds. The problem is that they don't produce the same blooms as were on the original plant that you got the seeds from. The blooms may be more like wild peonies, which are single flowers.
Wild peonies can be quite attractive in their own way, much as wild roses are, but they aren't the fancy double flowers that one usually thinks of when imagining peonies.
I would say go ahead and plant some of the seeds, just to see what kind of blooms you get. You can always buy some double-flowered plants to add to your garden. You may find that you like the ones you get from seed just as well.
This pic is of one type of wild peony. Some are prettier than others.