If yours is the inverter-based Honda 2200, then I wouldn't change anything. A lot of portable "generators" now are engines driving alternators that feed inverters.
I would ask first just how clean the output of this inverter is. Is it a true sine inverter? If it is, it probably has protection that prevents it from outputting unclean power (no voltage sags or frequency drifts).
If it is a "modified sine wave" inverter, it won't properly run many tools.
2200 watts/110v is 20 amps. But remember that circuit breakers are designed to trip at the rated amps. You can't pull more than about 80% of rated for very long. That's 16 amps. If you have a variable speed drill that shouldn't be a problem. A 7 1/4" circular saw that pulls 12 amps [unloaded and running speed] isn't going to work. You won't get it up to speed before the breakers trip.