It depends on the type of Solar you have.  There are 2 types, the cheaper 'modified sine wave' and more expensive 'pure sine wave' types.  A number of electrical items aren't too happy working with the cheaper type as the waveform of the output has harmonics that upset or destroy their sensitive electronic bits.  The more expensive type is suitable for anything as it is the same as what would be supplied from the electric companies.

That said, the problem will be that dishwashers run heating elements to heat the water and to dry the washing up.  This will suck the power from your batteries in no time.

You can lessen the load on the batteries by rigging up a pre heated water feed. As all machines only have a cold feed you could plumb in hot and cold through a temperature controlled mixer tap (like on a shower) so water into the machine is already at the desired temperature (40 or 60 degrees).  The water would be heated by whatever you have (gas/solar hot water) so the dishwasher wouldn't need to heat it up.  The only heating would then be at the end during the drying cycle.

Nigel