It is possible to run dual electrical systems, but given the amount of trouble, I don't think I'd bother.
Once you've mounted the 12-volt alternator and installed a 12-volt battery, you're not far from a complete conversion to 12-volts.
You'll end up replacing all the bulbs, and installing some voltage reducing resisters, but its not a huge project, and will be easier to maintain than a dual system.
