Yes, all results in the HCL returned showed 5.1 as supported. (VMware Compatibility Guide: System Search)
Regarding the storage, local is fine. If you cannot recreate the datastore from scratch, you will not receive 100% of the VMFS 5 functionality (but that doesn't mean that there is an issue in having it):
http://kb.vmware.com/kb/2003813
Here is the upgrade guide:
vSphere 5.1 Upgrade Guide: http://pubs.vmware.com/vsphere-51/topic/com.vmware.ICbase/PDF/vsphere-esxi-vcenter-server-51-upgrade-guide.pdf
I have no experience with the appliance, so I cannot speak to that.
-Brian