Non compete clauses?

I am currently with a company that has a clause that I cannot work with another company at the hospital I am at for at least one year after I leave their employment. I would like to stay at this hospital, but after having spoken with other travelers there, I find that they are making $9-10/hr more than my agency is paying me.
Can I go with another agency to do a new contract at this hospital without my current agency finding out?
Do agencies REALLY keep track of past employees that closely?
Thanks,
Trish