I don't believe so, but following because I had not considered this to be a potential issue.
My wife is a State of Florida employee and is required to make the mandatory contributions towards the Florida Retirement Investment Plan (as opposed to pension plan). Separately, she is maxing out her 403(b) account for the full $18k per year. Nobody indicated that it presented an issue, nor was there any reference to a conflict in the paperwork. The money ends up in two different places (myFRS for the former, Vanguard for the latter), although it all does end up invested in retirement accounts.
I can't imagine there would be a problem given that just doing the math to try to hit the max would be a huge headache, but I am interested to know if someone has more definite information on this. The distinction seems to hinge on whether the $18,000 limit is applicable only to voluntary contributions.