While op-amps are designed to reject noise and other disturbances in the supply rails, shifts in the supply voltage can affect the output of the op-amp.  Just how much the op-amp may be affected depends on a number of factors (noise, frequency, temperature, degree of change in voltage, etc). The op-amp’s power supply rejection ratio (or PSRR) can give a good estimation of how much an output can be affected by noise or changes in the supply rail.  The PSRR is frequency dependant so its value will change under different circumstances. The voltage delivered to the op-amp’s supply pins should be kept constant, within the manufacture’s specifications, and as noise free as possible.