You might. If you are lucky. Takes about 3 to 5 years for them to reach flowering size and what you get may look nothing like the original. fun though.

If you fancy the challenge then leave the seed to develop, the ripe seed is black and infertile seed is often bright pink.

That sounds like a fun project. Leave the seed pods on to ripen fully. When they turn brown & crisp, the seeds are ready. You'll need to put them in the refrigerator for 3 months. Then you can start them indoors and plant out in the Spring. I've done this with day lilies and this might be the year when they bloom.

paeony pods will split open when the seed is ripe. only select the black seeds.
Many paeonies undergo double germination.
the first year a root is produced and the following year you will get the shoots.
A friend grows from seed regularly. he sows then in a deep 'pan'/ tray and leaves them outside to get their winter chill and all he ever does is check for water and removes weed seed.

Thanks folks, your comments are much appreciated.