a/c unit and 2000 watt gen set
You've asked a good question. The manufacturer of the A/C unit should be able to tell you the "locked rotor amperage" rating for the compressor in the unit. The LRA is the maximum current the compressor will draw if it is not turning for any reason. If your generator can put out anywhere near that amount, it will be just fine.
The only way to know for sure is to try it. If the unit starts quickly and decisively (not laboring or sounding "iffy") and the generator doesn't seem to nearly stall, it should be fine.
The reason I say this is that while ratings are helpful, look at the transformer supplying your house and probably a few of your nieghbors. The rating on it is probably not enough to run every circuit in your house. I have seen 5 houses on a 10 or 15 KW transformer with electric heat in at least one house and it somehow works.
The other advice I'll give you is to keep the wire from the generator to the A/C as short as practical, at least 14 gauge (12 is better), with the least number of connections practical. Each connection is a potential voltage loss, as is each foot of wire. I have seen central air units wired to the legal minimum capacity that started fine in the morning, but would trip the circuit breakers later in the day when the voltage dipped a little and the units tried to restart.