Should I ask POI for update on PhD application?
It's perfectly fine to send such an email; academics are aware that candidates need to know these things.

Send a concise email explaining that you have an offer elsewhere (A) and ask when you will hear from B. 


  If I think hard enough


I know it's difficult, but try not to second guess the inner workings of admissions committees. It's much less stressful if you email them and ask.