Possible but irrelevant- steam engines are useless without coal. Trying to feed a steam-mill with lumber is less cost effective then just using a regular windmill.
Coincidentally, Europe has a lot of coal.
Where as this is out of the question entirely. You need so much technical and social change to pull this off, that to call the resulting society "Cathars" is at the very least misleading.
Catharism is a christian heresy, not a society. You might as well say it's misleading to call Catholicism Catholicism because it's undergone ~2000 years of change since the start.
Otherwise you will be left with one (or a couple) Gatling guns (designed by some ahead-of-his-time genius, already burned at the stake)
The Cathars really weren't big on killing people who disagreed with them, especially when compared to medieval Catholics.
and no ammo or personnel to run it after a few years.
With some talented blacksmiths and access to steel, which was created, albeit in small quantities, at the time, casting enough ammo to run a couple of guns would be very much within the realm of possibility, and training someone to use a gun, even a Gatling gun, is significantly easier than training someone to be a longbowman, which would probably be the closest medieval equivalent.