No Avamar can't do it. And right now (as of 6.1) backing up s-vmotioned vm's is not supported as i learned today :-(
So the question is if VMWARE allows to disable snapshots of vms that are performing a storage v-motion. And to disallow s-vmotion as long as a snapshots exists - like in Pre-vSphere 5
We like the automated feature of Storage DRS, and i would hate to disable it.