Actually, it depends on the pistol; if it is pre-1898 or whether the ATF has declared it to be a curio or relic and whether the stock is of the original style.
For instance, you may posess an original rounded stock for a Navy Luger, but you can't have the flat board "artillery" stock with it. You should keep the components cased together. Nothing in the law says you can shoot the gun with the stock attached, however. The ATF will send you a list of pistols and revolvers you can posess stocks for.