First to answer your question on bloodworms, Yes, they can eat them. Infact, all my fish that I've offered bloodworms to have enjoyed them alot, especially the bettas.
Peas are okay for him to eat, also, but not as his whole diet (of course, I knew you knew that^^!)
About the tropical fish food.. I would assume it would be okay. Though I've never done it myself, you could always compare the ingrediants of betta food and your tropical food to see how they vary.
I hope I was of some help. =)