I haven't tried but this is a very small battery. Very very small. There is a good chance it might try to open the garage door only to either burn up the APC or worse your garage door opener due to lack of amperes. When you have a load pulling more amps than a power supply can provide what generally happens is something gets smoked. If you were trying to get a portable way to open a garage door then I would get a large car battery, a 12v. power inverter (to convert the car battery to 120v AC.), and a cheap battery charger to refill the car battery. This will be more expensive but much safer and less chance of screwing up your garage door opener.
Before you spec out and buy your 12v power inverter look on your garage door opener for input current or wattage. If it is displayed in wattage take the number and divide by 110, this will tell you how many amps it pulls out of your wall. It'll probably be arourd 2 to 6 amps or so (I've never messed with a garage door but there are other factors at play that I cannot estimate like how heavy your door is and how much of a counterbalance you have aiding the lift.). Use that amp rating when deciding on a power inverter and make sure your inverter is 30% stronger than necessary to avoid smoking components.
I have spent a couple years doing work in electronic prototyping.