With the information provided, the only answer that can be given is a definite maybe. There are circumstances under which spoiled food is covered and situations where coverage is denied. If it is covered, you will only be able to claim a limited amount of loss, and that amount will be clearly defined in your policy. Since this amount varies by state, insurer, and policy, there is no way of knowing how much of your loss the insurance would pay.
If the spoilage is the result of a covered peril, such as a windstorm or water damage, then it will be covered by the insurance company as part of the losses. Your policy will either have a clause which limits the amount of coverage for spoilage, or spoilage will be tallied according to what you can prove your losses were, such as by presenting receipts to the insurance company.
If the power loss was due to a regional power failure such as a power plant going offline, you probably are not covered at all. Similarly, if the utility company cut off your power for some reason, such as not paying your bill, then you will not be covered because the loss of the food was due to your own negligence. Home insurance does not cover losses related to "acts of god" or personal negligence unless it is specifically written into the policy. Additionally, you may be able to purchase special riders to cover disasters like an earthquake, there is no such rider to cover spoilage of this type because doing so would open the insurance company to endless claims which may or may not be fraudulent, but which could not be proven in court.
The best solution, in this situation, is to have an alternative power supply available if the power goes out. When the lights are out, don't open the freezer or refrigerator any more than necessary, and if you do have an alternative power source, use it infrequently to make certain that your food is protected for as long as possible. If the amount of food that is in potential danger is relatively small, you could also consider cooking it to preserve it for a longer period of time if you have the ability to cook with gas or wood.