First let's make sure that your co-workers know the difference between cynicism and pessimism. Cynicism is a presumption of worst intentions (distrust of people), pessimism is a presumption of worst outcomes (distrust of situation).
That being said... Yes, it is possible to be too cynical.
There is an art to being truthful without being perceived as unfeeling or uncaring. It's a much an issue of how the words are spoken as it is the words themselves. There are also times when speaking an opinion, or even a fact for that matter, may be detrimental to the conversation.
In addition, it is possible to simply wear people out with cynicism/pessimism. There comes a time when people get tired of hearing "worst possibles" even though the words might be absolute fact and infallible truth. What you perceive as being honest they perceive as being grouchy, irritable, untrusting, and overly critical.
Finally, as to your last question, the answer is a resounding Yes. Always presuming worst possible outcomes and intentions limits you to that lens, often blinding you to the good in things and people. As with everything, balance is key. Being a cynic and a pessimist when it's merited is fine. Being a cynic and a pessimist by default isn't. Not only does it tend to drive people away, it isn't all that great for your physical health, either.
The saying "Expect the Best. Prepare for the Worst." really is the way to go. A balance of hopeful optimism and acknowledgement of potential negatives.
*Edit to add* Looks like Grandpa Shooter and I were posting pretty much the same thing at the same time.
Brad