Doubt you can do it on gov't dime....
I inquired with TMO in conjunction with my PCS about moving a non-running project race car. My intention was to tow it on a trailer with my truck and get paid for the weight...
TMO answer, they will ship car parts, not cars. So basically if you stripped it down to the shell they will pay for everything but the chassis. <My personal interpretation of the JTR.
TL;DR
No, unless you strip it to individual parts, IE bare chassis.