Is it possible to plant the blooms off hens and chicks like you would a seed? If this is confusing here's a picture of the blooms I'm talking about
I don't understand your question. Are you actually wanting to know if you can grow hens-and-chicks from seed? If so, yes you can (at least the ones with viable seed).
"Planting the blooms" doesn't make sense though, at least not to me anyways.
BTW, if you want more of the same type of hens-and-chicks as you started with (assuming you start with a cultivar, rather than a species type plant), dividing the plant (transplanting some chicks) would be the way to go.