[CentOS] Two labels, one mount point

I have a systemd mount unit that mounts an external drive by label. What happens if I plug in two USB external drives formatted with the same label? Does the last one discovered mount on top?

I'm rotating backup drives and the backup software assumes the drive to be at a particular directory. Normally I'd stop the service, umount the drive (via systemd stop), unplug, plug the other one in, then start the service. (An automount unit will mount the replacement drive when the service touches the mount point.)

But I'm wondering what happens if someone isn't careful and plugs in the 2nd drive before shutting down the service and removing the first one.