There may be DC voltage variations (generally, a momentary drop in voltage) which occur under certain conditions due to the inadequacy of the power supply . but there should be no internal "power spikes" (i.e. increases in the DC voltage) if the circuit is designed correctly.
Separate circuits alone will not protect against this, but separate circuits with some form of power isolation/filtration or their own power supplies are generally very effective and often used, especially when there is a digital circuit in a component along with analogue components.
Regards...