I can't really think of a way to do this - especially if your drop down list entries are hard coded. Even if they are from a secondary data source, it may take a bit of trickery.
For example, you could have a SharePoint list for the employees. And a combo box in your form that uses that list as the data source for its entries.
Promote the field that is bound to the combo box. Add a custom workflow to the library you are submitting your form to that runs when a new item is added - the workflow could have logic to add the employee name to the list if it is not already there.
But, of course, this is supposing you are using SharePoint at all.