But I would advise against it as turning the power off to net boxes etc without shuting them down is usually a bad idea!
Depends on the box. I've got a ChromeCast and it couldn't care less if power is yanked.
It does indeed, My Net box however very much dislikes abrupt power outages :p
It corupts the system on mine and means I have to reinstall everything

Personally I would also get peed off with the thing shutting off mid programme or whatever

Though I do commend the OP's idea!!
If you want to go ahead with it though you need to get a low voltage coil timer relay that is capable of switching 240v. Then wire it so the coin mech activates the timer coil with a retaining contact so it stays energised until the time is up.
Then use one of the switched contacts to switch your 240V to your android box adapter.
Or if you plan on running it off a standalone supply switch that.