There are several on electric guitars. They vibrate, but it's not a huge amount of energy.
The human ear is non-linear, so it's actually quite quiet, just louder than the body itself, and you are creating a flat-plate resonator which is quite efficient, so demonstrates how
little the body is vibrating as in terms of energy, it's a tiny fraction of the energy transfer of an ABG. It's a long time since I've tested it, though, to see how it might affect sustain. That might have to wait until I've moved and I have a table again. You can get a boost from resting the head of the instrument onto a wall, but there it's reducing the vibration of the neck by increasing stiffness, meaning more is heard from the strings. I am not sure to what extent resting it on the table is amplifying the signal from the body of the guitar or increasing overall stiffness. I'd have to think about how that could be tested. The issue is it might increase sound transfer (shortening sustain as it is robbed from the string) at the same time as increasing system stiffness (increasing sustain) so if sustain remained the same I might not know what had happened. I could put a contact mic on the body and if the signal dropped it might mean less transfer from the string (increased system stiffness) but then I'd also need to calculate the energy difference which means I'd need to weigh my table and a bass with all the hardware and neck taken off and assume the density was much the same. I might try with the Les Paul guitar kit as it's mahogany just like my coffee table

I have to build it, though.