Yes, but in these situations, how much power would the HVAC really be drawing when ambient temperatures are pretty close to the desired room temperatures? Humidity is obviously a different issue. But in the case of rain, the utility isn't going to be offline for 4 days is it?
Most Gulf Coast residents do not consider high 80s-low 90s F with relative humidity above 90% (the prevailing day-time conditions during nearly seven days of continuous rain) to be "pretty close to room temperature."
In flooded areas/neighborhoods, electrical distribution utilities routinely isolate circuits to minimize electrocution risks and damage to their infrastructure. Assuming minimal wind damage, the duration of the outages are a function of how long it takes the water to recede and safety checks to be completed.
Natural gas distribution is generally much less affected which (along with propane grills) is how many cook during electrical outages; Generac, Kohler, etc. sell a lot of whole-house NG generators after each named storm, but most residents still rely on gasoline-fired generators for powering lighting, fans, and refrigeration appliances.
Particularly after Rita and Ike, many commercial and service sites (gas stations, water & sewer districts, hospitals) now have dual fuel (NG & diesel) fired generators.
The various technologies for back-up power systems all have trade-offs, but it is mostly economics. If cell costs continue to decline, batteries will become an increasingly viable alternative, but politicians are going to play it safe and lean more towards the worst than the the most likely case.