Welcome to the forum RiceBurner, this question has simple answers and complex answers. One simple answer is probably no, the average "normal" UPS might have say 500W capacity with 20 minutes or so at max power output. Your stoker will be using around 150W to 280W depending on where it is in the cycle and whether the Tstat is calling for heat.
You need to look at the specs for whatever UPS you are considering and remember Watts = Amps times Volts, my Harman is run by a Coal-Trol so my power usage is totally different from yours. Depending on load (damp coal, oversize coal etc) the stoker motor needs around 1 amp when it is running (120W) the convection blower needs around .8 Amps (96W), the combustion blower needs around .6 amps (72W), and the power supply that runs the Tstat relay and timers uses a small amount. This is where the answers start to get more complicated, it depends on how much these motors are running to determine the length of time your unit will run on a given UPS. Av8r posted some info on the APC 1400W UPS that can be wired to extra batteries. You could run a 120V outlet to the stove and put the UPS and associated extra batteries in the basement or other remote location (now the answer gets even more complex
In the final analysis the simple answer is to install a small UPS if you already have one and run some experiments and see how long it runs. If your experience with power outages in your area show that power will not be out for long usually, then you might have an easy solution. If not then you need to look at other more complex solutions. If you do a search on UPS in the forum you will find many posts on this topic.
Best wishes for finding an easy answer, keep us posted.