xYUL departures are domestic arrivals at MIA because you will have pre-cleared CBP at YUL. Therefore, neither I-T-I nor the post-CBP bag drop process. Your bag will be checked at YUL straight through to BCN and you will not reclaim it at MIA at all.

Depending on the reason for the misconnect and AA's systems, your bag may or may not be pulled from the BCN flight if you do not board, but most likely it will head onward to BCN and you will simply claim it at BCN when you eventually arrive or the bag will be retagged to your new itinerary and held.

If you ask AA to reticket you to MIA, as part of that process, AA will have the bag sent over to baggage claim. This will likely take several hours, but refaring a YUL-BCN ticket to YUL-MIA and eliminating a segment, calculating the fees and then subtracting out the new fare will take a while as well. If you know about this in advance, you may find it easier to deal with it in advance.