Yes, however when you go into the vault all of the key fragments will be converted into the key for that vault. So if you want to spread your key fragments around, then place them in your bank and only use 60/150 at a time.

Old ones will combine with new ones fortunately. It still takes 150 fragments for a key to WGT/ICP vaults and 60 for others(which is silly because they only stack to 60 and clog my inventory) too. They're also all BOE now so you can sell/buy them easily.