Will PSU with Active PFC (Corsair CX600M) work with "Stepped approximation to a sinewave" UPS (APC BX1400U-MS)?

[Lukman]

I want to buy a UPS, but having a very limited budget, the only one that I can afford that can provide my need is BX1400U-MS. However, after doing some further research, I found that my PSU (Corsair CX600M) most likely has APFC, and people say that I need a pure sinewave UPS so it won't cause problems and possibly damages my PSU.
So, I was wondering if anyone here has some experience with BX1400U-MS or any simulated sinewave UPS from APC and APFC PSU for that matter. I just want to know if it will work when On Battery. I don't need the UPS to keep my system running for a long time, but just enough for me to turn it off or hibernate it, but I've even heard some say that simulated sinewave UPS wouldn't work AT ALL On Battery with an APFC PSU, like when there's a power outage, the PSU will automatically shut down.
I just don't want to empty my thin wallet for something that won't work.