Yes, you can upgrade.
It might be easier to do if your ticket is not on your room key, which you can ask for when you check in.
Just take your tickets to a Guest Relations window at the first theme park you visit when you arrive and tell them you want to upgrade. It doesn't matter when you upgrade, as long as you do it before the MYW ticket expires, but your AP will be back-dated to the first day you used the MYW ticket, so you might as well get the AP as soon as possible.
APs are also much easier to replace if you lose them, which is another reason to do the upgrade as soon as you have the chance.
The cost to upgrade will be the difference between the MYW ticket you're upgrading and the cost of a new AP.
Prices here:
http://allearsnet.com/pl/ticketchart.htm