The gun will be registered as a Short Barreled Rifle. The stock is just a componant. Registering one Glock as an SBR, installing the stock, and then swapping that stock to one of your Title I Glock handguns would be a recipe for a federal felony.
Be aware that registering your Title I Glock handgun as a Title II Short-Barreled Rifle means that you have to follow the same rules with it (whether configured as a rifle or a handgun) as you would with a machine gun or other Title II weapon. Even without the stock on it, you cannot allow others to borrow it, have to be careful how you sell it, and cannot cross state lines with it without filing a form 5320.20 ahead of time, etc.
It isn't a minefield, exactly, but you do need to be careful to know and follow the rules.