If you did not purchase the transfers from the cruise line, DO NOT put your cruise line tags on your bags until after you've claimed them at the airport. You cruise docs should tell you this.
I'm not sure what would happen. They might claim your bags anyway. They might not. If you're counting on them to transfer your bags, you could have a problem if they don't. Similarly, if they grab your bags because they have the cruise line tags on, you could waste a lot of time looking for them.
The basic rule of thumb is to put the cruise line tags on the bags right before the step where they take control of them. If you've paid for transfers, that will be before you get on the plane (assuming you arrive during the hours they collect luggage). If you're driving to the port yourself, put the tags on before you drop the luggage with the porters at the port.
Again, you docs should explain exactly what they want you to do with the luggage tags.