Yes, you can upgrade your tickets anytime within the first 14 days after first use -- even if you've used all the days.
If you bought the ticket from a discount broker (like
undercover tourist), use the tickets to enter a park before doing the upgrade. This will give you the best price advantage for your upgrade. Unused tickets are treated as an exchange, and you'll only get credit for what Disney was paid for the ticket. Used tickets are treated as an upgrade, and you'll get the current full gate price of the ticket applied to the upgrade.
The date of the annual pass will be back-dated to the date you first use the ticket. So, there's no advantage or disadvantage of doing the upgrade on the first or last day of your trip. Do it whenever you have time to get around to it. (Just so long as you do it within 14 days of first use.)
If your Magic Your Way tickets have the Water Park Fun & More option on them, you can upgrade to either the Annual Pass or Premium Annual Pass so long as you don't use the ticket for a WPF&M admission. If you have used the ticket to enter a WPF&M attraction, you can only exchange it for a Premium Annual Pass.
You can do the upgrade at any guest relations window. There is one inside and outside the gates at each park, including the water parks. There are also two locations at Downtown Disney.
Resort Concierges cannot do this transaction -- their software can't do anything that deals with an annual pass.
Don't forget to take your blue
DVC membership card and a photo ID with you when doing the upgrade. This is the only way to get your DVC discount. Each adult must show an ID that matches the address of the DVC member.