600 DC AMPS gives you 300 as a working amount since you don't want to go below 50%. 300 amps x 12 volts =3600 watts. If ONE A/C draws say 15 AC amps that is 15 x 120 or 1800 watts so you could run it for an hour or two. Start up loads are roughly double or 3600 watts briefly which is the real bugaboo and could trip the
inverter.
Assuming there is circuit breaker protection on you Prosine nd it is well ventilated...you could try it without risk. Just have everything else off when you do! You also will be generating heat and losing efficiency even if it does work and I know of no one who does this. I assume your dock electricity is free compared to your diesel and that is why you are considering this. I don't think doing this is worth the 50 cents worth of diesel you'll save as you probably have other things you need your batteries for.