If the voltage was marginal (say in a brown-out), and things were 'on the edge' of accepability, it could draw excessive current and trip or blow a safety device. When I had my air handler/a-c unit installed, I installed a low-voltage cutout device. I think it was made by IDS. It's about the size of a deck of cards, has some controls on it to set the desired operating range, some LED indicators, and an internal relay to disable operation if the power is outside of parameters you set. No idea if it has saved my system, but it also has a time-out after power outages to prevent operation immediately after power reapplication when it can fluctuate radically for a few moments or so, thus further protecting things while the voltage is all wacky until it stabilizes. The internal motors probably would be okay, but the unit has at least a couple of circuit boards, and not asking them to operate until the power is stable is probably a good thing.