Yes, you can trade-in a partially-used MYW ticket toward the purchase of a new AP. You even used the correct term - "trade-in."
"Upgrade" is what you call it when you turn in a MYW pass before the 14-day window passes. In the case of an upgrade, you would get the full purchase price of the original ticket applied to the cost of the new AP, and the new AP would be backdated to the first day you used the MYW ticket.
"Trade-in" is what happens after the 14-day window passes. Trade-ins can only be done with MYW passes that have the no-expiry option. In a trade-in, you would turn in your partially-used MYW ticket and recieve a credit for the part of the ticket that's unused. The credit depends on 1) How much the ticket cost when it was purchased, and 2) How much of the ticket is left unused. I don't know how Disney compuites the value, but suffice ti to say that the value is more favorable to them than to the Guest. In a trade-in, the AP will start on teh day of the trade-in.
If you have a MYW pass that you have not used at all, then you can do an upgrade. The AP will start on the day you do the upgrade.
If you have a MYW pass that you bought from a ticket broker, such as Maple Leaf,
Undercover Tourist, or TicketMania, the upgrade or trade-in value of the ticket will be based on
what the broker paid DIsney for the ticket, NOT on what you paid the broker for the ticket! Tickets from brokers have substantially less upgrade and trade-in value than a ticket bought directly from Disney.
If you have a ticket without the no-expiry option, you can upgrade any time before the ticket expires. You can even upgrade before you even use part of the ticket. When you use part of the ticket, the 14-day expiration period begins, after which the ticket expires - and once it expires, it has no value and cannot be upgraded or traded in.
Upgrades and trade-ins can ONLY be done at WDW; you must go to any Ticket Sales or Guest Relations window at the 4 theme parks. Upgrades and trade-ins cannot bedone at the
Disney Store, online, by phone, or at the resorts - only at the theme parks.