Should I tell other companies about my situation now?

I am working in a university and decided to look for a job with higher pay, and I told my supervisor about it. She decided to give me a raise, just a few thousand lower than the market value, which I didn't expect it at all. With the benefits and work-life balance I currently have, I think it's a pretty good deal.

Since I sent out the resume, lots of recruiters and companies showed interest and would like to interview me. Since the decision making of salary raise involves several levels of people in the university, I don't know when it will be final. If it goes final, I will stay with my current job. Should I tell other companies about my situation now?

Any input will be highly appreciated!!