Ok, did some more tests.
This VM has 2 disks :
ide0: local:909/vm-909-disk-3.qcow2,cache=unsafe,size=42G
ide1: local:909/vm-909-disk-2.raw,format=raw,cache=unsafe,size=165G
- ide0 (system disk. A WSUS server) can move successfully, live. Probably VM stopped, did not try that.
- ide1 doesn't...