Hi and welcome BES!
First you have to make sure the seniors apartment allows dogs. Then you know residents who live there should expect a reasonable amount of barking.
In my experience, Yorkies bark LESS than other breeds (including my Shih Tzu and Sheppard-Husky mix dogs)! Much less! But that's my Yorkie dog - maybe I got lucky with him not barking.
If the puppy doesn't already have a barking issue - then s/he should not develop one when with you. When my three pups get playing and start barking too much - I get my little spray bottle out and squirt them once or twice. They stop barking real quick. Good luck and please keep us posted.