Would a small home inverter power lights after an EMP?
How are you going to power the inverter? Do you have a generator? Do you have stored fuel on hand? A small inverter can only power so much (100w is one lightbulb). Forget powering a fridge.
A generator is noisy, but has the power to drive most equipment in your home. But again, how much fuel do you have on hand, and the noise will attract others seeking to take it from you. A good bet is to use an inverter plugged into your vehicle, if you vehicle still operates. (I own several vintage 1960s and 1970s cars, with spare voltage coils and such to keep them running, with full gas tanks.) You can run your car to power lights, and others won't notice as they would with a generator. Get a bank of batteries, install a voltage regulator, and keep them charged from the grid until needed, then recharge from solar panels or generator if main power is out.