Indeed, all you need to take to a gig is two workbenches and a concrete floor.
To really do a proper experiment, you'd need to use the same bridge and headstock and attach them to long thin pieces of wood of similar dimensions and perform a full spectrum analysis of the output.
The strings, pickups, and electronics will be the most significant influencers of tone (assuming that the material used for body and neck is adequately rigid). The wood used to connect them will have some effect, it's the amount of that effect that is questionable. My feeling is that it's close to negligible, others (mentioning no names) will differ.