As coalberner said there could be fumes, but chances are if the run from the stove to the power vent is short enough the gases will escape. Remember the fire will go out since the stoker and combustion fan are not working as well.
I have an Alaska stoker in the kitchen using a SWG power vent located on the wall right above the stove. We had a couple power outages last year, both times the stove went out and the CO detector did not register alarm levels. This year I have a digital CO detector and I purposely shut off the stove and watched for CO right by the stove. It only went up to 14 ppm.
So bottom line, a inverter with a built in battery charger and deep cycle battery is a good idea but probably not essential. Just count on relighting the stove if the outage is more than an hour or so.