Does it matter if engine power goes through the gearbox before the clutch, or through the clutch before the gearbox?
I'm not sure if there has to be a specific order of clutch & gearbox, or if it's just a matter of what's easier to manufacture.
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If you were to put the clutch after the gearbox, you would likely need a far bigger clutch due to the much larger torque that it would need to transmit.
Pulling away even on level ground would be like trying to do a hill start in a 'normal' car.
Other than that I can't see any reason why a gearbox couldn't be designed to have the clutch on it's output. As long as the clutch allows the gears to sync when changing gear, it should work.