It is not up to UA to "honor". It will be up to the carrier on which you are rebooked to determine. The general answer is No, that other carrier will not "honor" the allowance & waiver you would have had on UA and you will likely need to pay whatever fees are involved.

Nonetheless:
1. If the other carrier tries to collect a fee, ask the bag check agent whether they will waive the fee. They are not obligated to do so, but you should ask. Not worth asking in advance.
2, If you do have to pay, submit the receipt to UA for reimbursement. UA will not generally reimburse, but may issue some token customer service gesture.

Remember that your alternative is to decline rebooking on the other carrier and to wait for the next available service on UA. Generally a poor idea, but worth considering if it is a short wait and you are looking a high fees.