About the only 6 volt things that would not survive 12 volts very long are light bulbs (seconds of life, if that), and the fuel gauge (a few minutes). Longer term, a 6 volt wiper motor won't hold up to 10 - 20 manures of constant operation (they run really fast until the smoke fills the truck cab). Starters and charging system will fail eventually (depending on their original condition). I may have missed a few things, but you get the drift.

My son and I cruised a 48 Dodge (definitely 6 volt system) with a 12 volt battery up and down the road in front of our house for many hours (for about 10 minute streak each time) over a period of about a month with a 12 volt battery strapped in.

Some information sources state the 6 volt to 12 volt conversion in the Dodge truck division occurred between either the 54 to 55 model year or the 55 to 56 model year, or the 56 to 57 model year. I guess you get to pick your time frame.