Hi,
No, shared storage is not required:
| Array/ vendor types | Requires same storage replication solution at both sites (eg. EMC RecoverPoint, NetApp vFiler, IBM SVC, etc) | Can support any storage solution at either end including local storage as long as it is covered by the vSphere HCL |
SRM - Array Based Replication vs. vSphere Replication | VMware vSphere Blog - VMware Blogs
Michael.