False.
OP, go on your account online. Click on the upgrade function for the line you're upgrading. Then, you'll see two amounts listed - one is what's remaining to become eligible for trade-in upgrade, the other is to pay off the entire remaining balance of the current phone. If you want to trade-in, simply choose that option and go through the process of selecting a new phone to "upgrade" to (don't worry, you're not actually upgrading).
Once you've chosen a new "phone", you'll come to a screen where you have to pay the remaining installment in a separate transaction with your credit card. Pay that amount and then immediately cancel the rest of the "upgrade".
You are now eligible for upgrade/pre-order. 🙂