Generally yes, at any Guest Relations counter (at a park or at Downtown Disney).
It is suggested that some usage of the subject ticket, if that kind of ticket is still being sold*, be made before you upgrade; this causes the correct value of the subject ticket towards your annual pass to be the price of that ticket as sold at the ticket booths.
The correct start date for the AP is:
o The date of the AP's issuance if a used ticket was not submitted towards purchase,
o The first usage date of the submitted ticket if the latter was used,
o The day after the previous AP expired if the new AP is a renewal of an AP.
Inspect your new AP to be sure the start date is correct. Once in awhile a mistake is made.
Note: Tickets used more than 13 days ago may not be modified or upgraded.
* Pre-2005 tickets may only be applied to an annual pass or other ticket if they are totally unused. It is not clear at this time what the rules are for non-expiring post-2004 tickets since these are no longer sold at the ticket booths.