Yes, in most cases you will be told, although how quickly depends on the supplier the room came from. When a hotel releases a room it has already confirmed, which usually happens because the property is overbooked or has closed part of the building for repairs, the supplier sends a cancellation back through the booking connection. Your portal picks that up and the booking status changes from confirmed to cancelled, so your team can see it without having to phone the hotel.
The honest part is the timing. Some suppliers report this within minutes, some only during their own office hours, and a small number of properties do not tell anybody until the guest is standing at the desk. That last case is not common, but it is the reason we suggest your team looks again at any booking made a long way ahead, and any booking at an unusually low rate, as the arrival date gets closer.
What comes back to your customer is normally everything they paid for the room, because the cancellation came from the hotel side and not from them. Rebooking is a separate job. The portal will not go and find another room on its own, so somebody on your team has to search again and confirm the new stay, and the room you find may not cost the same as the one that was lost.
If this matters to the way you work, ask us which of your hotel suppliers pass cancellations back automatically and which do not, and set up an alert on your side so a change in status reaches a person instead of sitting on a screen nobody is watching.