Oct. 2012 - Sandy Super Storm.  8 days without power.   After 4 days we went to South Jersey to a hotel by my son.  He was some 30 miles from the center storm landing and they only got rain.   He never lost power, no lines for gas, business as usual.  So after a few days there I took his generator (3500K) he got a day before the super storm and I hook it up to run the UPS for the stove.  I did plug in a surge protector and the ground light light up.  I did not have any ground wire going any were from the generator.  So I plug in the UPS and it started.  I started the pellet stove and TV, only to watch DVDs' and we ran trough lots of stuff on the DVR.  No cable and limited cell (basic phone/text only) It ran some lights too.  Gas was available around the corner, if you waited on a short line.

So if your generator / AC converter can be passed throught a surge protector and get a ground light to come on, it can then work throught a UPS.  You should ALWAYS plug a pellet stove into a UPS even if it's a $100 special.  Those little blips of lights going out will shut off your stove mid fire and smoke up the house.  PLUS, it keep those surges away from the stove controller.  No UPS will work if there is no ground and only a few will turn on if there is no power.  So you can't just charge the 12V battery and expect the UPS to run for 10 hours again as it won't turn on.

Replacement UPS batteries (every 4 or 5 years) are available from various places, .  WELL WORTH THE PROTECTION.

Nov. 2011 - UPDATE

DO NOT HOOK UP A WHITFIELD PELLET STOVE TO A GENERATOR OR DC CONVERTER (Car battery converter to AC) unless they are "pure sine wave".  Yes, they work but when you turn it off and try it the next day... it will not work and you'll get weird lights going on/off. 
After you plug into "real" AC you will have to press the start button a few times to straight out the controller !  A few people have confirmed this as well as my 14 year old unit.

SO until I can find out this problem... no "modified sine wave" converters until I check this problem out.   I tried a UPS into my DC converter but without a "real" ground no UPS will start.  A UPS will smooth out AC current.

If you need to run your stove on non-AC power.  Get a "pure sine wave" converter.  This company sells a 300W version that will work with 200W (aprox) left for a light or whatever.  Go to https://www.theinverterstore.com/

There are small "sine wave" generators that work 8 hours per fill.  Again, the UPS will keep the stove running when you turn off the generator to fill it.