I'd say not a good idea for several reasons:
Almost guaranteed to scratch a finish no matter how careful you are.
More stuff to deal with when going under a vehicle.
Likely to catch on things under the vehicle, or get caught under a crawler wheel.
I'd say if you need tools handy, make up a tool roll that will hold what you need, and load it as you need them. Make it from denim, and pad the outer main layer of the roll and you can unroll it on a fender and not be too worried about scratches.
Not quite sure how to best deal with sockets, that would be partly driven by how you store them. if you use rail and clips you could make one pocket to fit one rail and make that the "center" of the roll...