(inverter repairs) Does reverse polarity can kill power MOSFETs in UPS inverters?
Without schematics (I recommend some reverse-engineering on your part) It could depend on the topology but in general a reverse polarity will flow through the body diodes on all the FETs, and without current limitation these will go up in smoke. 

If the designers didn’t implement any reverse polarity protection, every single IC on the circuit became a forward-biased diode, if you are lucky only the regulator blew-up in this condition. . But the FETs will probably connect directly to the battery through the low-impedance windings of a transformer. 

I am not sure of what standards apply to the battery side of an UPS, but I would consider not having some sort of fuse/breaker for the battery connection rather unsafe. Given that you did not see any physical damage or smoke, it is very likely that there is a fuse on the PCB that you have not recognized.