"Is it okay to do so (uninstall any and all mail server applications)?"
The users on your desktop communicate with each other through sendmail. For example, when a cron job fails cron sends a message to root that there was a problem in cron. If you are running without sendmail it means that you will have a harder time fixing some of the problems with your system because you won't have all of the error messages.
Be prepared. Create a LifeBoat CD.