No, you currently cannot process mileage upgrades on AA.com. Maybe someday. However, given how long it took the programmers to make eVIPs visible on AA.com, I'm not hopeful that it will be in the foreseeable future.
With regard to the fees, you are confusing two different fees. There is a $20 phone reservations fee but it does NOT apply to reissues. So, if the original ticket has already been issued, the $20 fee will not apply if you call in with the PNR code to do the upgrade afterwards.
There is also an "award fee" (formerly the "expedite fee") that applies when you claim an award out of a non-EXP account within 21 days of travel.