Can the hot water heating system be left on with the main water valve shut off while on vacation?

In most cases, yes. As long as the sytstem has no leaks, and is up to operating pressure(usually between 12 and 20 psi) when the main water is shut off, you should be just fine. Just to be safe, have somebody check the house on a daily basis while you are gone, and give them the number of your preferred plumber/boiler tech, just in case a problem should arise.
Have a great vacation. Lee.