I installed one for our bedroom AC....we only use that AC for our cats when temps head up over 90°. All 3 of our ACs draw 12 amps.
I did before and after tests with the soft start using my 3300 generator. Before the SS, when the AC compressor hits, it is obviously all at once....the generator has to immediately raise RPM to compensate. After the SS, it will start to raise RPM slowly...when the compressor hits, I can't hardly hear it in the genny. I have all of the monitoring equipment in place to follow the draws before and after, and even graphed the difference in genny surges...and it is very impressive.
Assuming a 12A draw when running, your genny is fine once the compressor is spooled up...but that initial hit will be hard on your genny and it will run fairly hard with the constant ~1500W/12A draw. I'm also assuming you're using a 15A extension cord which will apply more resistance into the system.
As you progress with running your AC on gen power, always look forward to the 3K gensets with a shorter 30A cord...it makes life so much easier with the 3K gennys loping along running the AC (and all other appliances) instead of the high demand/noise level/gas tank fillups/etc of your 2K genny.