Yes - everything except the BT TV Extra & Sport Channels and BT Player will still work. Any recordings made of extra channels however will stop working when your subscription stops.
Don’t you have to have had it over 12 months to be able to keep it? (I have had mine 4 1/2 years so will be keeping mine)
Once it's delivered it's yours but finishing a contract early will involve cancellation charges which I assume would be higher if in the initial contract period when the box was supplied