This depends actually more on the inverter's specs than anything.
Compressor motors as a general rule don't like to start with MSW (modified sine wave).
If the inverter is pure sine, it won't be an issue at all. I can start mine with a 1400VA ("900W") pure sine UPS unit, no problem.
Throw my "750W" (1500 "surge") MSW inverter at it and it causes the inverter to trip out on overload, even though "by the book", it is capable of handling it.
Now if you can get it running somehow FIRST...
The other issue is startup surge. That compressor, even though rated at 1.2A, that is RLA (running loaded amps). Start requirements are more intense, and are usually indicated by an LRA designation (locked rotor amps), which can be 10-20x the RLA, so you might be looking at as high as 20A or more for a fraction of a second, but your 3kW will not see that as an issue. And actually, 3kW may even be powerful enough to be able to start it even if it
IS an MSW (but I'd bet its a pure sine).
If you are in fact dealing with an MSW inverter, there are ways to "trick" it into starting motors such as those found in compressors; sometimes that work, sometimes don't. Let's just say you're not the first to run up against this.
Best way to find out? Try it. It will either work or it won't.
Steve