I did something very similar a couple of months ago.
Our Veeam servers are on a different subnet to the ESXi mgmt traffic, so I created a new network using unused NICs on the Veeam servers, and NFS vmkernel ports on each ESXi server.
At first all the traffic tried to go through the standard Veeam server LAN connection, until I read this thread:vmware-vsphere-f24/how-to-use-veeam-vpower-nfs-server-t10342-15.html
The Veeam repositories have to be setup as static NFS datastores on the ESXi servers, then the traffic will go through the correct NICs.
I had to add the registry entry mentioned later in the thread manually to each Veeam server.
NFS performance is still an issue for us, but that may be related to other factors.