Many of them have audio alarms that will warn you that power is off. Some can be set up to turn off the alarm. I'm not sure if there are ones that will only turn on the alarm whenl the battery gets low.
Some UPS's and inverters put out a "modified sine wave" or "stepped approximation to sine wave." These terms are deceptive. They're more of a modified square wave than a modified sine wave.
Last time I looked, the ResMed S9 machines said modified sine wave (MSW) was OK, but don't say whether it's OK for the A10 machines. I've never been able to find Philips Respironics documentation that says yes or no for MSW.
It's probably OK, but I'm not sure.
More and more modern devices have problems working with MSW voltage from UPS's or inverters due to ill advised nanny state regulations about power factor correction.
BTW, if you want to test whether your CPAP will work with a UPS, you need to unplug the AC cord from the wall. Most UPS's are "standby" mode and just connect the output to the AC from the wall unless the wall power is off.
There are "pure sine wave" inverters/UPS's that put out a more normal voltage waveform, but they cost more money, and I suspect they're less efficient, especially at low power drains.