I am on Lexapro, which is similar to Celexa but generally considered to have fewer/more mild side effects. (But really, the only way to figure out which med is right for you--if any at all--is kind of trial and error) I am on it for anxiety/panic and OCD, as well as depression.
Once i stabilized, and figured out what dose was right for me, and most of the side effects had cleared up...no, I had no problems with it and my training. The only effect it had was make me able to leave the house so I COULD train. The side effects CAN take a while to go away, though, up to a few months. In the end, the only lasting issues I have had are a decrease in libido (but I already had that form The Pill) and sort of a low-level sinus/allergy type thing. I have not had any real weight issues...but Lexapro is not known for weight gain (although, as far as SSRIs go, Celexa sort of is).
You didn't mention what type of doctor was making the recommendation, but if you haven't seen a therapist/mental health practitioner before trying meds, I would do that. GPs are great, but the only person I would try meds from is a mental health professional. And I would also try and work with them first to see if non-medicinal options existed for treatment (talk therapy, CBT, accupuncture, etc.).
mmm-mmm-Momo Charms Handmade beverage charms, jewelry, and miscellanea http://momocharms.wordpress.com