I absolutely agree that telling them would harm your work life. Some will suddenly say you're a poor worker (god help you if you've been late once or twice) and not living up to your potential, and use that as an excuse to fire you, and if you take them to court, it's up to you to prove they fired you over your mental illness. All these laws to protect us from unscrupulous employers, and it's almost impossible to put into effect!

Telling anyone--co-workers, friends, family, acquaintances--that you have a mental illness opens you up for judgement, even if they don't intend to.