You can get a list of VM's with an engineer tag name because they are tagged directly to a VM. You probably want to do a search for the Category of "OS Support Engineer". You probably want to put together a quick Power-CLI script using the Get-TagCategory , Get-TagAssignment and Get-Tag cmdlets.
You can probably search for a blank "" field on VM's with no TagCategory of "OS Support Engineer". If you need help with the powershell I can give it a go, but it's not my strongest skill. You could ask in the Power-CLI forum?
With the cardinality, I'm not sure once it's set you can change it. I think you'd have to get rid of the Category and re-import it. I'm not 100% on this one, it would require a little testing!