If my research is addiction related, can I tell the professor I have first hand experience? I’m an undergraduate doing research in the bioinformatics department, and we are researching drug addiction. We are also attempting to incorporate the psychology cooccurrences (i.e. suicide ideation, anxiety, depression)  of addiction. Personally I have not experienced drug addiction, but I am very familiar with two different addictions (one ongoing) and the cooccurrences mentioned above. 

A benefit of this has been that my first paper and project was very well received by the professor because I understood the subtleties of the topic. However, this also means I am mentally unhealthy. 

I have always considered telling the professor about this, but I don’t know if this would be encouraged/acceptable, and if I would still be allowed to stay in this research area.

Any input is appreciated, thank you!
Yes you can.  Even may.  

The question is should you?  What is the motivation? To brag your worldliness?  To earn pity?  

I advise no.  Concentrate on learning the topic academically.  Let your personal experience enrich your learning but more as deep background.