Certainly, OB trucks often have stuff running on general purpose computers these days- they just tend to build them into sturdy rackmount chassis, and make sure it's all physically assembled properly.
Maybe if you could mount a small 4u or 6u rack in the sleeper, and stand a usably-sized LCD on top of it when it's running (and packed in a suitable Peli case or something when it wasn't), you'd probably be ok. A laptop would still be easier, of course, but you will be paying for the convenience.
The biggest physical danger is if you have a large CPU cooler- especially on a PC that is upright in a tower stylee. The forces on the heatsink, which is already screwed down to the CPU core firmly, can cause it to crush the CPU core, which isn't ideal. So if you do go with a "normal" PC, try to keep the motherboard horizontal.
Have you considered a small form factor machine, like a Micro ATX one? There are some really good gaming-centric Micro ATX motherboards around now, which can take full sized GPUs and proper desktop CPUs. If you just wanted a "normal" PC, a small form factor box, that would give you pretty high performance gaming in a smaller box.
Not running it while you're moving is a big thing too- even if you're using spinning rusty glass hard drives instead of SSD, a powered down and parked hard drive can take a lot more Gs than you can before it dies
