Ypu can tow with a sjort bed. The trade off is,,,,,,
You loose 2 feet of useable cargo space,
You cannot carry a sheet of plywood or sheetrock with the tail gate closed,
You may need or want a much heavier slider hitch, thereby reducing your available cargo capacity,
You likely could not fit the truck with a folding bed cover,
Rarely have I ever seen a 3500 short bed truck. Which indicates to me your interested in a 2500 series truck? Which is fine as long as your looking at a short, light fiver. Once you go over about 12,000 pounds gross your going to want a 3500 series truck.