It depends on what kind of reverse supply protection was used.
If it's a crowbar diode, bad things could happen if you beat on it like that 60 times a second. A crowbar is meant only for shorting a reversed DC supply.
If it's a series diode, though, you just get half-wave rectification through the diode. That and the op-amp rail caps combine to make a poor-quality unregulated DC power supply. I'd expect the amp to work in this situation, just with a lot of ripple on the rails, if the resulting voltage were high enough.
If there's no reverse protection, the chips are all fried. Dead, dead, dead.