Not exactly. There’s a ratio of RPMs of the drive motor to the specific input of the alternator that generates the correct frequency. It depends on the way the alternator is designed (ie number of poles) that will yield the correct frequency, almost like a gear ratio, that is optimized for efficiency, and power plants have to constantly make slight adjustments to the drive motor speed the keep the frequency exact (usually done automatically within the drive control system).
I’ve never seen frequency be an issue in a residential system, but in theory it could happen.