Storage Live Migration is officially supported since RHV 3.2 that allowed migration of virtual machine disks to different storage devices while the virtual machine is running.
RHV 3.3 added the ability to do it to several disks of the same vm concurrently.
RHV 3.4 added the ability to do cold move between any two storage domains in the same DC (e.g., NFS and iSCSI) and Storage Live Migration between types of file domains (NFS/POSIX/Gluster) or block domains (FCP/iSCSI).
RHV 3.5 added the option to move an entire storage domain between DCs or even between setups.