That is a good strategy if you a rapport with the manager and don't plan on bidding or taking over the job. It gives you an idea on what your market is and how to bid other commercial accounts appropriately while knowing a little about your competition.
I don't think it is a good approach is you are seriously wanting the job and the manager knows you want the job. I highly doubt you would be getting 100% honest answers. You come off as being desperate. They might be thinking "If he is so great and busy, why is he coming around trying to steal jobs"
A different approach could be simply asking if their current service to their satisfaction.
Beating the current companies bid by a few dollars isn't going to get you far if they are already satisfied with who they are using