Prevent Event Registration for a Specific Role (Drupal)
You can do this with a custom extension - I recommend checking out the documentation for hook_civicrm_aclGroup and maybe for hook_civicrm_permission as well - the second hook will give you an easy UI to control which roles can't register.  The good news is that this is a simple extension as these things go - maybe 30 lines of code should do you.

Without a custom extension, there's no way to do this that I can think of.  However, consider a) having a separate login for each user, and b) installing the No Overwrite extension as alternatives to mitigate this issue.