Yes, it has been done, but you need to factor in the distortion power factor (not displacement) for running the VFD when sizing the UPS. I used a .8pf and it worked fine for me. So take the kW of that motor (7.5 / .746 = 10kW) divided by .8pf = 12.5 kVA on your UPS loading, along with whatever other loads you need to power for that length of time. I was powering a 10HP HVAC unit on a remote radar site and we had to keep it running for 2 hours to allow service people to get there with a portable generator. Worked great.
But here's a hint; if all the rest of your loads are 1 phase at that site, compare the price of using a 3 phase UPS and a 7.5HP VFD, to using a larger 1 phase UPS and a 15HP VFD. By larger I mean take your 12.5kVA and multiply by 1.732 = 21kVA, plus your other loads. The VFD will provide the 3 phase for the motor from that 1 phase supply and a 1 phase UPS is significantly less expensive than a 3 phase UPS. I found that doing it with the larger 1 phase UPS and larger VFD was still significantly less expensive. I think the reason was that 1 phase UPSs are priced for more "commercial" projects and therefore more competitively, whereas 3 phase UPSs are usually more industrial and the suppliers think they can get a better price on them. Can't hurt to check it out. Report back what you find if you don't mind, I'd like to know if it still works out that way.