Virtualising Backup Exec and backing up to NAS?

Background: we are a small school with 3 VM hosts running Hyper-V and 9/10 virtual servers. Only physical servers apart from those are a DC and a backup server

I've got some money to buy a storage appliance of some sort. I could go down the route of having a SAN for VM Storage but to be honest local storage has been doing a fine job until now, with Veeam backing up so able to do a quick(ish) restore in case of disaster.

So instead I was thinking it may be a better idea to replace a huge clunky old tower I have acting as the backup server, that currently has a RAID5 array and a few USB drives attached.

Would it be feasible to buy a QNAP NAS/SAN and run it as NAS, with Backup Exec on a VM backing up to it? I already duplicate it to a server at another site so not being able to use the USB drives wouldn't be a huge issue. More wondering whether speeds are going to suffer too much backing up to a NAS?