Summarize, as there are sib-cases
If you check bags with anyone but UA, you not receive the Chase bag benefit. This is also true if you purchased a "bag bundle" from UA (that will be refunded and should be automatic). And if an UA elite, you will receive the benefit that carrier offers to *A elites, not UA's benefit. WIll do no good to argue at check-in, pay and deal with UA later.

If your ticket gets re-booked due to an advance UA schedule change and you have to pay for bags that would have been free if you had checked-in with UA -- you can ask for a refund, unlikely, but may get a few miles/ETC in consideration. You will have to request this but the farther in advance of travel the less likely this becomes. Having some status may help.

If you get re-booked the day of travel, irrops, your refund request will be treated better -- such as an ETC for a little more than the bag fees. Again you will have to request this after your travel is finished.