Try a few- what could it hurt to experiment? It has been my experience that everything does better planted directly in the ground- but many have good luck with container gardening...Happy Gardening!
I can picture them vining up the ropes holding your container - i think it'd be cool to try but that you'd either want to keep unvining them so they hang down, or hang your basket low so you can reach all the peas!
You might do better with one of the bush snap peas. If you pick the peas young before the peas form in the pods they taste about the same. Snap peas are all hybrids and have some snow pea in their genetic makeup.