It would be just like unplugging it, it will take a while but shouldn't have too much build up of gases, once the blowers shut down, the fire normally goes down quickly, it will still burn for a while but very minimal.
You should look at a back up power supply. We have discussed this in previous posts. Do a Search on "Backup Power" or battery back up.
Depending on how long you need it to run, depends on the size of the backup power supply. Some are much more expensive then others depending on the output.
I have a small computer UPS (uninterruptable power supply) 800-900watt hooked to the stove, it lasts for 10-15 mins+, we normally don't experience extended outages. (yet!)
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