My roof cooler leaked into the ceiling. Is that covered?
If the failure was sudden, generally yes. If the unit had been leaking slowly over weeks or a season, that is gradual damage and most policies exclude it. The practical difference is whether anyone had looked at it recently, which is why the seasonal startup matters.
Should I switch to refrigerated air?
That is a comfort and cost decision rather than an insurance one, though it does remove a water line from above your ceiling. If you are replacing the system anyway, that is a genuine secondary benefit worth knowing about.
We are away all summer. Does that change things?
It raises the risk considerably, because a small leak runs unnoticed for months and ends up looking like gradual damage. If the house sits empty, shutting the water supply to the cooler is the single most useful thing to do.