Disclaimer: I'm not a lawyer and you are 100% responsible for knowing and following all federal and state firearm laws. Don't risk a firearm related felony with a 10 year minimum sentence purely on advice from random people on the internet. Do. Your. Own. Research.

That being said, yes, adding a stock would make your "pistol" into a "short barreled rifle" and you would need to file a Form 1 with the ATF, engrave your firearm with all required information, and get your approved Form 1 back (with stamp) BEFORE you can add a shoulder stock to your pistol. Even owning a stock for your Zenish pistol before you have an approved Form 1 could make you a felon by constructive possession. So tread carefully. The laws are dumb, and the chance of getting caught is low, but it's 100% not worth fucking up the rest of your life over. The whole point of an arm brace is that the ATF currently does not consider it to be a shoulder stock and it doesn't change the classification of your firearm. In other words, you can put an arm brace on your Zenith pistol and the ATF still considers it a pistol rather than a short barreled rifle.