I am going to say yes, but if we start looking at many months, things can get a little tricky with water being the especially difficult one, in part because around here wells run about 500' deep. We do have some ponds on our property, and one is joint with the neighbors that appear to be spring fed as they have water all year round, but fetching water, especially by foot, would be a significant chore.
The buildings are on gravity septic, so we should be good for a while with that, especially as normal use from things like washing machines, dishwashers, and showers would be minimal or even moved outside.
The house has a generator that could run for a good length of time, maintaining even AC or it could be rationed to a couple of hours a day and last a lot longer. This would keep the freezers going for quite a while, but at some point, one would have to find a way to preserve in mass whatever you can from them.
In the greater community, a lot of the area around here is dedicated to agriculture and a few local farms could provide enough to feed the community, but some form of trade / exchange would need to be figured out. However, if we're getting to this point, we're also at the point where roving raiders are going to be a problem and community security will be necessary, which could be part of that trade as even the farmers need to sleep.
So, short answer, yes, I think we would be fine for a month, if not several, but we'd be looking at bigger (area wide) problems by that point.