If AY still lets you put in an AA number in the right field for the trip involving the upgraded AY flight, then the AY-operated flight posts (if at all) as per the rules listed on aa.com for the fare type purchased and in the same time frame as normal for AY-coded-and-operated flights.

AA-coded flights operated by AY post to AA accounts within a few days time. Last several times this year, AA-coded flights operated by AY have been posting quite often no later than 3-4 days.