Yes, overthinking can lead to a mental condition. People generally think about negative parts of their lives, which can cause depression. Over thinking can cause anxiety disorder, it can also lead to obsessive compulsive disorder. Over thinking is associated with schizophrenia.
Too much thinking sometimes, is a symptom of a mental illness. Most people with mental conditions spend more time in their head than spending time with people or their environment.
A person's mental, and ultimately physical health is certainly affected by their way of thinking. If a negative outlook is a person's typical response to everyday life she/he is more likely to become depressed about negative outcomes than someone with a generaally optimistic mindset. We all have to face the occasional setback or rejection, but ruminating at length about the misery that has caused you will not help the situation and will inhibit or prevent opportunities for new incidents which could prove positive.
A person who constantly dwells on the unsuccessful aspects of his life and assumes the worst is unlikely to be good company or attract positive opportunities. How can such a person convince others that she/he will fulfil a task competently (or at all) let alone add colour to any social event?