We've had a long standing issue with our users entering in Catholic Charities as their organization name when registering for events, making donations, etc. It's caused havoc in our system as we will have many people associated with the Catholic Charities record, instead of their appropriate organization (e.g. Catholic Charities of New York). We've used the auto complete extension to show users a set list of organizations they can choose from, however we still get people simply typing in Catholic Charities, despite our best efforts (we still allow people to put other organization names, because people outside our network sometimes register for certain trainings, make donations, etc). Is there a way for the system to throw back a warning/error to the user and/or force them to change their organization name if it detects Catholic Charities was input as the value?
The exact behaviour you describe would be possible but will have to be custom development. It would be specific to your organization and website.
However I do think you will be able to achieve something like what you want with the CiviRules extension. You would be able to 'catch' the new contact as a trigger (individual is added) and use the field value comparison condition to check the value of the current employer (or alternatively catch the new relationship Employer of). CiviRules would allow you to then create an activity for a team member, alerting him/her to the problem. It is not perfect, but sounds like an alternative without custom development.