Rapaire comments that the incomplete nourishment provided by MREs shouldn't be a problem, which is true; but the main point I meant to emphasise is that the preservatives may be toxic to some persons within a very short time if you don't have enough other food to clear the system - and especially if you don't drink enough water. If you plan to rely on them for more than one or two meals, perhaps you should try eating them for a period comparable to your intended "emergency" use before you're stressed out by a real emergency, so that you know your limits.
I have seen people who brought MREs to festival and ate only MREs for as little as three days puff up and turn red (flushed) and lose all interest in getting out and about. The first symptoms weren't too bothersome to them, but were obvious to everyone else; and they'd have contributed little if we had needed them for anything very strenuous.
The suggestion that anyone relying on their freezer should consider a generator is probably a good one, but a bit of research I did recently on the possibility of adding one to our camping kit wasn't too encouraging. The small ones generally need at least a gallon or two of fuel per hour, and refueling every 3 to 5 hours. Safely storing enough fuel even for a week of intermittent use is problematic. In many areas, if about half the people decide to evacuate they'll take all of the accessible local fuel supply with them, and you may not be able to go get a couple of gallons.
The "web opinion" also is that the small units aren't really all that reliable, even allowing for the tendency that those who've had problems are much more likely to post.
Installed generating units, with their own propane or diesel fuel storage or off natural gas (relatively, but not completely, immune to interruption) are rather expensive and hard to justify unless you're in an area where there are frequent interruptions. Not the sort of expense you'd want for a "might happen once someday" sort of thing if there are alternatives.
If you're considering a generator, do your research carefully. And consider that a reasonably full freezer should last about a week without power if you're careful about how often you open it up.