If you do the storage migration from XO, you shouldn't have to do anything.
XAPI does refuse to move a disk while CBT is on, as @jr-m4 said, but reading XO's code it catches that refusal, turns CBT off on the VM's disks and retries.
The price to pay is that the next backup of that VM is a full one, and the backup job switches CBT back on.
The other trade-offs are in the docs (https://docs.xen-orchestra.com/backups-and-dr/backup-types/incremental_backups#purge-snapshot-data-cbt) : NBD has to be enabled, snapshot retention has to be 0, and since the purged snapshot only keeps metadata you can't roll back to it.