You wouldn't be upgrading at all. If you've paid off the entire phone balance before the minimum 12 payment limit, you own it outright. You can then walk in and sign up for a new phone under a new upgrade plan at any time you wish. But you'd have nothing to trade in under the program and could keep your existing phone, recycle it for store credit, sell it yourself or whatever you wished.
It would be the same as any installment plan - pay off the balance early, the device is yours, to do with as you please. And since you've fulfilled the terms of your contract without exercising your upgrade option with a balance owning, you'd effectively now be a new, first time subscriber to the upgrade program when you purchased a new device.
There is no rational point to even enrolling in the upgrade program if you're just going to buy the phone outright as soon as you get it.