Yes, I told my coworkers. I am so glad I did because they now understand I am essentially responsible for my children by myself makes them very understanding and I really appreciate the support. I will also mention, the more people you open up to the more people who you will find going through the same thing. Addiction is everywhere.
I will say I have worked at my job for a very long time and am close with my coworkers. I also told my boss. However, if you are not ready that it totally ok.