No. You get all 1st tier (A1, B1, C1) prizes and can manufacture (claim) them as long as you have enough tokens. After you do 1st tier (manufacture then research) you can do the respective 2nd tier (A1 -> A2 etc.). Basically - you can get all the prizes at badge level D (for Zaxx, Jack and MA), if you have enough tokens. But you need to do them in order. Only research that adds new prizes is unlocking a new client (Red Mage for example) but AFAIR that requires badge C. Missions do not unlock prizes.