Since the vSphere C# Client also uses the vSphere API itself, a user with proper credentials to the vSphere environment can easily download the client from an alternative source and still login. Of course, there are ways of preventing this such as restricting application installation on end users desktop but there is some amount of management overhead of identifying those existing and new users, especially if access is delegated out to other teams.
There is a very simple solution if you choose to block ALL users from using the vSphere C# Client which requires a tiny modification on the vCenter Server itself and it takes effect immediately with no service restarts.
Disclaimer: This is probably not officially supported by VMware, use at your own risk.
Login to your vCenter Server and locate a file called version.txt
Windows: C:\ProgramData\VMware\VMware VirtualCenter\docRoot\clientThere is parameter called exactVersion which will be set to current supported version of the vSphere C# Client which should also match the version of your vCenter Server. You just need to change this to some other value that you know will not exist in your environment such as 9.0.0. Once you have made this change, now when a user tries to connect and there is a miss-match in the version, the vCenter Server will provide you with a download to the vSphere C# Client located on the server as it normally would if you did not have the latest client.
Now, even though this prevents users from logging into the vSphere C# Client, users will still be able to connect using the vSphere API which includes the use of vCLI/ESXCLI, PowerCLI, vCO, SDKs, etc. and the use of the vSphere Web Client for either vSphere 5.0 or 5.1 will continue to work. Ideally, it would be nice to be able to control this access on a per user/group basis and perhaps even specify how a user can connect whether that is through the use of the APIs or UI only. Is this even useful to have at all? Would love to hear your comments.
For now, if you want users to get familiar with the new vSphere Web Client 5.1 ... this is one way of "encouraging" them ;)