If you're talking about using the inverter as a UPS, where the cord is being installed to supply power (ie. "shore power") when the power is on, but then instantly switch to backup battery power if the power goes out to keep your computer or whatever else running, then yes, you can do that provided you don't overload the circuit. If you're plugging it into a 15 amp outlet, don't have more than 15 amps worth of stuff plugged into it; with a 20 amp outlet, the limit is 20 amps worth of stuff.
If you're talking about putting a cord on the output side of the inverter so that when the power goes out you can plug it into an outlet to backfeed power into your house outlet and power some of the circuits in the house from the inverter, that *can* be done but you have some major limitations and critical steps to follow. First, you'd have to go to the circuit panel and shut off the main breaker to the house. That will separate the house from the power grid so you won't be generating dangerous voltages on the grid through the transformer that could hurt a power company lineman working on the lines. It will also prevent the inverter from being blown up when the power comes back on and tries cramming voltage back into the output. Second, whatever outlet you'd plug that into is on a circuit breaker connected to a main bus that runs half the breakers in your house. But that one outlet is rated for a maximum of 15 amps (most typically) and the romex cable in the wall is rated for a maximum of 15 amps, and the circuit breaker it's on is a maximum of 15 amps. So everything being used on every circuit of that half of the house circuit panel couldn't exceed 15 amps (or again, 20 amps if it happens to be a 20 amp circuit). You'd just be better off using the inverter as it's intended and only running things you can plug into it directly, or better yet get a whole house generator installed.