Yeah it can work! I love both cats and dogs, but my husband is allergic to cats! We love Yorkies 1st and formost of course...
But why don't you double-date...
that is introduce your yorkie to THE CATS! and see if they all get along. If not, then maybe you have to think hard...Which is most important my yorkie, or my boyfriend OR your boyfriend has to think which is more important my cats or my girlfriend! Good luck!!!