Maybe. But marriage licenses are usually public records anyway. (and you appear to be using your real name as a screen name on this public forum.) Do you live in a Community Property State?
They will find out someone else claimed her as a dependent if you file a joint return. They won't know why and the IRS won't tell them. However, they (and you) will receive separate correspondence from the IRS to determine which return is correct.
Time to fess up?
But if I file separately, and she does not file. When her parents claim her as a dependent will they receive a correspondence from the IRS?
If you file separately (never the best filing status) and she doesn't file, they will have no reason to know.
Still time to fess up?
The answer is no. If you file MFS and they claim her as a dependent and can do so (because she has no filing requirement) then there will be nothing from the IRS to indicate that she got married.