There's two main problems with using different batteries:
- The UPS will probably not be able to assess how much charge the batteries have. This may lead to it not working at all, or it might not care in the least. Given the ultra-cheap brand I would expect that the UPS has the most minimally complicated methods of measuring capacity (charge voltage) and wouldn't care what battery you strapped to it.
Batteries have three main measurements: voltage, capacity, discharge rate (based on internal resistance and stuff only electrical engineers care about). You have to "match" all three or it wont work.
- Most lead-acid batteries have six internal cells, about 2v each, giving them an overall charge of 12 volts. It's also common to find 6v batteries in small applications (usually lawn mowers and mopeds). I have also seen 18v, 24v, and 48v batteries (usually in large power equipment - like large UPSes and photovoltaic installations - or in specialty applications - many airplanes have 24v batteries).
- The "1.2Ah" and "7Ah" ratings are the capacity - I've also seen this expressed as Watts (as pictured below).
- The charge/discharge rate is usually indicated in multiples of "C" (ie "10C") where C is the capacity - I've also seen this expressed in the time it takes to fully charge/discharge as in the picture below). A battery having 7Ah of energy would be plenty of capacity for your UPS, but if the discharge rate is 0.1C you can't discharge that capacity any faster than 10 hours - totally useless for a UPS (when you try to draw too much the voltage just drops off and the USP will go into a failure mode). Similarly a rating of 10C means it could be discharged in 6 minutes.
A battery from a UPS showing the ratings (12v, 45W, 10m; aka 12v, 3.75Ah, 6C):
Good manufacturers will clearly state at least these three ratings. If they don't you run. Also, if the price is notably cheaper than most they're probably lying about the ratings (most commonly the charge/discharge rating).
A cheap battery with some pretty lousy ratings (12v, 8Ah, 1.2A; aka 12v, 8Ah, 0.15C):
TL;DR Get batteries that are manufacturer approved, or don't be surprised when the UPS doesn't work.
Disclaimer: It should be really hard to do, but I'm sure there's some combination of wrong batteries might lead to the batteries bursting, possibly leading to a fire, chemicals going everywhere, and all sorts of fun.