The seeds you buy in the grocery store are of a variety commonly called the "Breadseed Poppy". This type of poppy is indeed Papaver Somniferum, and will produce fluffy flowers and decent sized pods. As long as the seeds have not been cooked, they will still grow. Culinary seeds however are often not as viable as commercial seeds, but chances are you will still get a decent germination rate from them. The quality and potency can also vary greatly.

But in the end, it's better than nothing! And if you're only growing poppies for their beauty as a flower, then they're a perfect place to start.

So if you can't find any at the flower shop, just go to the spice rack!