Everything I have read about PM docs leads me to believe that the drug screens that they do are very thorough. First, to make sure that you're not using any illegal drugs or pain meds not prescribed to you by them. Also, they check to see if you are taking your meds exactly as they were prescribed. If your pain is worse than usual one day, you're supposed to call in and tell them before you take extra meds.
My opinion, which is probably worth about as much as you paid for it, is that yes they definitely can tell the difference between hydro and oxy and yes they will check. A lab analysis easily detects the difference between oxy and hydro because a percentage of both are eliminated in their original form and they are also metabolized to more active forms in the liver, oxymorphone and hydromorphone, respectively.