FWIW, we ran our Harman stove off of a couple of different "cheap" inverters, I doubt they had a clean sine wave, and had no problems.
As I recall, the power draw was fairly high when the stove with lighting, but not in operation. Depending on what you are trying to do, you might be able to get by with a smaller UPS, assuming that you don't need to have the stove light the pellets (you can always do the manual ignition in a pinch).
Keep in mind that most UPS batteries won't last more than a few years. If you are going to rely on the UPS, I would suggest doing a manual test of it every few months to give the batteries some discharge cycles, and also to ensure that they are still good enough to handle a large discharge current without running down unexpectedly. I've seen too many cases where someone puts a UPS in, and it gets little use for a couple of years and then in the first major outage it runs down in 15 minutes.
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