The VMWare feature you are referring to is called "vMotion", which is made available by their vSphere product. From their website, VMotion lets you:
Eliminate application downtime from planned server maintenance by migrating running virtual machines between hosts.
So you're correct in thinking that
- if it's the host infrastructure that needed maintenance, and
- if your University is using VMWhare vSphere, and
- if the daily maintenance is done in phases that keeps other hosts up, and
- if there were enough of those other hosts, and
- if the operations was designed, configured, and staffed for this, and
- then its certainly possible that vMotion would let you continue to have access to VMs while maintenance was performed.
But that's an awful lot of speculation. Why don't you just ask them what they are really doing for six hours each night, and what you could do to help make sure some systems are still available?