It would work but I see lots of problems. First, if this is a fairly modern diesel engine you don't want to idle it "for hours". This will result in fuel dilution of your oil. You need to speed up the idle to about 1,000 RPM minimum to avoid "wet stacking".
Alternators aren't really designed for long periods at high outputs. Any alternator that will produce that much power at 1,000 RPM will likely be very large, you might even be looking at needing 2 alternators. Either way, overheating of the alternator, particularly with a stationary truck in hot weather could be a problem.
A 200 amp hour battery bank is probably pretty small for this application. If the air conditioner requires the full 3,000 watts of the inverter to start (and it well might) that's nearly 300 amps on the DC side. Even if your alternator is supplying 100 it might be hard to get that much out of a 200 AH battery. Really, a starting battery might even be a better application.
I'd go with a much larger battery bank.
In the end this is likely to be more expensive, use more fuel, and be louder than a Honda generator. Why do you object to the Honda? (or Yamaha for that matter?)
If this is a diesel truck I would do what the big rigs do, get a diesel powered Auxillary Power Unit (APU) and run that to power your AC.