Most homes in the U.S. are fed through a split phase transformer (aka a single phase, center tapped transformer). The center tap is the neutral, and you get 120 volts from either line to neutral, and 240 volts from line to line. One transformer will typically feed three or four homes.
The two lines and the neutral come into your breaker box. In a typical breaker box, the connections alternate, so a 120 volt breaker just connects to one connection, and a 240 volt breaker connects to two connections and gets one connection to each line for 240 volts. Also, since they alternate, this tends to load balance the house, with roughly half of the 120 volt breakers on line 1 and the other half on line 2.
By backfeeding into one line, you are at best powering half of the house. If you don’t turn off the main breaker, you are also backfeeding the one line all the way to the transformer and out to the other homes that are fed by that transformer, and you’ll even be putting some power onto the main distribution line that will try to feed other homes in your neighborhood. As was previously mentioned, it’s also a shock hazard to any linemen out there working. Most of those wires aren’t insulated.
You’re also going to have some current that is going to go out through the line you are powering, through the transformer, and into the other line and back into your house. It won’t have enough current to power the things on the other half of your home’s breakers, and some devices might actually be harmed by such a small current level. Fan motors, for example, will just sit there and get hot since there will be enough current to heat the wires but not enough current to spin the motors.
When the AC comes back on, it’s going to be at a certain point in its AC cycle and your small generator will be at another point in its AC cycle. Since the power company’s line has much more current capability, it’s going to win and it is going to try to force your small generator almost instantly into sync. Hopefully the breaker on your inverter works, because otherwise you’re talking a whole lot of smoke.
It is much better to just run a few extension cords through your house to the devices that you want to power. Then it’s safe and you’re not backfeeding into anything. If you insist on using a suicide cord, make sure you turn off the main breaker, and it’s also a good idea to turn off all of the breakers that go to anything that you aren’t using.