They can go a while without filtration. It is helpful if you have a battery operated air pump or can otherwise keep the water aerated. This is a time where I'd use a dose of Prime or something like it to keep the ammonia in check. If you can, make sure you have a way to keep the water temp stable. Some people use heat packs like the ones used for winter sports. You can wrap blankets or other insulation around the tank and possibly the filter.
When my power went out in a storm for 5.5 hours last month, I rigged a double boiler arrangement on the gas stove which I could light with a match. Every half hour I poured some warmed tank water into the tank. I let it dribble to get some air in it. I never let the water temp vary more than a degree. I only have a 29 gallon tank and it was a lot of work, but my fish came through fine as did my benficial bacteria which are in a canister filter on the floor. In my case we had no heat, but the heat from keeping a big pot of water simmering on the stove kept the main part of the house at 65 F. I keep my tank at 76 F.
Your large tank is a blessing. It will take a while for the temp to drop. A multiday power outage will be difficult and it will help to have people who can take shifts to keep the fish alive. I was looking at staying up all night when our power came back. I was grateful I didn't have to do that. I had no other help.