Companies are not going to drug test you if they aren't planning on hiring you. It's an added expense. Heck, I worked for one that made us reimburse them for our background and drug screen with our first paycheck (if you failed either then they covered it). This same company was eager to get me started but was waiting on my references (small hospital being the holdup) that knew they were going to be contacted. It took almost a month.
A couple years ago, when starting with a large hospital they used a third party to do background verification. Extremely thorough too. Took about three weeks for everything to clear but in the waiting period I was drug screened, HR processed on policies/procedures, and picture taken for my badge (which I was secretly doing the pee pee dance during because I thought the screening would be done first and I was holding it then for a few hours!). I guess since screenings were required for nursing school
every quarter and I was just background checked to take my boards they figured as long as my employment history was accurate they were safe.
In another week if you still don't hear anything it wouldn't hurt to call.