If the 6 VMs are already powered on, then DRS will try to separate them as much as it can. Then it will display a DRS fault that it couldn't fix an anti-affinity rule violation, but will not power any of them off:
If 4 of the 6 are on and running on different hosts, and you try to power on one of the remaining 2, the DRS rule will refuse to power it on and give you this error:
The obvious downside is you won't have all 6 running. It is conceivable that if you had them running before the rule was created then they would stay running, but it is pretty much inevitable that they will be powered off at some point eventually for some reason or another and not able to start up again due to the rule. According to the capture they are off so they wouldn't be able to power all 6 on (actually there are 8 in the rule in the capture so 4 that would remain off).
An alternative solution (untested) would allow all of the VMs to be powered on, but you would still have at least 2 VMs running on 2 of the hosts, not meeting the client's impossible need given the resources:
You could create 2 "Separate VMs" DRS rules putting VMs 1-4 in one and 5-6 in another. This would allow all 6 to be powered on, but losing or powering down a host for maintenance would also mean you could run 5 VMs max, which is still better than the 4 you could run in the original solution even with all hosts operational.
Best Answer
For VDI (VMware View), my recommendation is to enable HA on your cluster as with any virtualized workload. That's a key feature of vSphere and makes sense to have on.
For DRS, understand your workload a bit. How many hosts will you have? How many VMs? How tight is the consolidation?
I'd say that the activity on virtualized desktops is not as predictable as an environment comprised entirely of servers. Spiky on the resource side. My understanding is that it makes sense to lower the DRS policy to "Conservative" to only migrate systems based on maintenance needs if you have a high level of consolidation. If not, possibly use the default or slightly more aggressive DRS automation setting.
Also see: Best Practices: Configuration of VMware vSphere DRS with VDI