Your question is not clear to me (it may be clear to others).
As I understand it, frequency and phase angle are independent of each other. If you want to extract the frequency, then the phase angle does not come into the picture. The frequency is simply reported as a number, for example, 60.183 Hz. This is an absolute number, not relative to anything else. So it is not important if the measurement scheme includes a phase shift relative to the zero crossing point. It will not affect the result.
On the other hand, if you want to measure a phase angle, or phase shift, then this is a relative measurement, comparing one signal to another. In this case, you would have to measure the zero crossing time accurately for signal A and for signal B, and then compute the time difference between them.
As a matter of practicality, if a generator is connected to the grid, then it is locked to the grid frequency, and there can be no difference between the generator frequency and the grid frequency. However, there will be a phase shift between the generator and the grid. If the generator leads the grid it will be delivering power to the grid (normal and expected situation). If the generator lags the grid, it will be sucking power from the grid, and will be motoring (unexpected and undesirable). If the generator has no phase angle with the grid at all, then it will be idling, and this will generally be an unstable situation to be avoided (a trip is likely to follow).
So in the real world, the generator has to be "pushing" at the grid, delivering power, and running with a phase angle ahead of the grid. By knowing the power delivered, the grid voltage, the excitation voltage on the generator, and other parameters, then there are equations that will indicate the phase angle that exists.
I dare say, it may also be possible to measure the rotational angle of the generator shaft, and compare this with the zero crossing point on the grid, and this would also give the phase angle between the generator and the grid. Maybe an EE could comment on this? (I am not an EE, so do not consider me an expert on any of this.)