I've seen guys use it to haul their SS, even the flare side (narrower box) is suitable. Just strap the bike down on a diagonal and leave the tailgate down. I think the rear tire sat in the hollow between the bed and the tailgate so very little weight was actually on the gate.
Having said that, I have a much better option for you. Get a used minivan. That's what I did and there are quite a few people using this method at track days. They are cheaper to buy and run, more versatile, easier to load, keeps things dry, more comfortable/easier/cheaper than a tent to camp out in. I can fit my bike and two extra people inside if I want to. Plus use it to take a boatload of friends skiing, or haul 4x8 sheets of whatever. Try that with a pickup and you'll be looking at a $40 000+ V8 monster.
If you insist on buying new, Dodge Caravans are listed in the $20 000 range. There are some things to consider like hatch opening height, and strap down points but nothing insurmountable. I just don't see the sense in pickups unless you're driving through trails a lot.