Calculating gains for Op-amps with real AC voltages
HarrisonO - I suppose, I know what you really mean. (By the way, what in your opinion is a "real" AC voltage?).

My answer: No - the gain is not varying with time.
For AC signals it makes no sense to find the ratio Vout/Vin for momentary values of both signals. Instead, the gain is defined for mean values of the sinusoidal signals - more  correct: For "root mean square rms" (magnitude ratio).

This applies to all amplifiers - single BJT stages or opamps, which in all cases are operated with signal negative feedback (and not open-loop).
Because all amplfiers contain reactive elements, it is - in addition - common practice not only to calculate (or simulate) the magnitude ratio but also to find the phase shift between input and output.

The existence of a frequency-dependent phase shift is another argument against the usage of momentary values for finding the gain.