Only if you already invested several grand in a 3D printer. A service like shapeways is similar cost and time to getting a pcb made. A pcb milling game machine is the same cost as a 3D printer.
You're again overestimating costs. A perfectly capable 3D printer can easily be had for under $500 and serves many more purposes than just fabbing PCBs. Many, many places (including libraries now) have 3D printers available for use at low cost. A mini mill capable of milling a PCB is harder to come by and also not useful for much more than basic engraving.
PCBs are over an order of magnitude more expensive and generally have a two week lead time unless you fab them yourself on a cnc or laser setup. Also, what do you do if you realize you messed up something in your PCB setup? You have to wait for a whole new batch or else toss it and wire manually anyway. With 3D printing, you just modify the model and print a new version in a couple hours.
For one-off prototypes like this a custom PCB is a really iffy proposition.