Let's start with if this is technically possible, that is if American has an e-ticket interline agreement with United, or can issue paper tickets on United. Per expertflyer, AA has the ability to do both, so their computer systems could issue a ticket.
The second question is whether or not they would do this. The contract of carriage describes their obligations: https://www.aa.com/i18n/customer-service/support/conditions-of-carriage.jsp
This isn't an operational change, but if it were and delays your arrival more than 4 hours, you'd be entitled to a refund, but they say that they will try to accommodate you.
For Force Majeure (weather, and other things they can't control), they say that refund is your only remedy but that they will also try to accommodate you. Note that they consider public health emergencies and labor strikes to be in this category.
For oversold flights, they say that they will "do our best to get those customers on the next possible flight", presumably because they are required to give you cash for the amount of time you are delayed, and putting you on another carrier can limit how much they have to pay.
For other delays that they cause, generally due to mechanical issues, especially an overnight, they promise to cover the cost of a hotel if they can't get you on a flight or give you a refund.
So just from the contract of carriage, they only promise to put you on the next possible flight if it's due to involuntary denied boarding.
This information is consistent with what travel agents are allowed to do when there's a problem caused by IROPS (mechanical, weather, crew timeouts, etc.): https://saleslink.aa.com/en-US/documents/Archives/TravelNotice/Schedule%20Irregularity%20(IROPS).pdf
Back to your question, depending on the reason for the delay, it's possible that AA will hold the outbound flight so that there's not a misconnect. If they decide to not hold the flight, then you're only guaranteed to be booked on another American flight. American can technically put you on the United flight, so now let's look at the likelihood that they will.
At least as of 2018, American publicly stated that their policy is to only put you on another airline if you have elite status, and only if you're delayed more than five hours if you aren't Concierge Key, Executive Platinum or Platinum Pro. Since you would be delayed more than five hours, you have a reasonable chance if you've qualified for any status in their frequent flyer program.
If you don't have this status, the agent would be bending the rules to accommodate you on another airline. Sometimes being very nice to an agent having a bad day can help, and sometimes making the request from an airport lounge can help too, but I wouldn't count on it.
If you think it's probable that you'll misconnect and you don't have American frequent flyer status, I'd be prepared to be stuck in the connection city until the next flight.