Regardless of what state you are in, it is your job duties that determine whether you are correctly exempt or not. If you are exempt, you are not entitled to overtime (an employer MAY pay it, but is not required to.) On the other hand, you must get paid your full salary every week, except in some very specific circumstances, regardless of how many hours you work. Yes, in the circumstances you describe, and again assuming that you are correctly exempt, they can charge the client for your overtime without paying it to you.
You have not provided anywhere near enough information to determine if you are correctly exempt or no, but you can check out the Federal DOL web site at
www.dol.gov and you should find some additional information there.
