Two case studies suggest that certain serotonin reuptake inhibitors may reduce sperm motility. My first thought was, "do these guys need another, literal kick in the jimmy?" But in truth, I doubt it would make a whole helluva a lot of difference to them.
Antidepressants frequently inhibit sexual desire. Depression itself is more likely to inhibit any desire to do anything about that sexual desire. Social interaction is almost completely beyond your abilities, and masturbation, if you can be bothered, often leaves you feeling worse than you did before you started. It's sometimes the price a victim chooses to pay, give up a meaningful sex life for a chance at a meaningful life.
This case study suggests that under certain circumstances, it's possible that one would lose the ability to have children by treating their depression. To some, the idea of being without children would easily overpower the SSRI that they were using in treatment. The disease would key into that primordial instinct, propagate the species, and use it to overcome the drugs. For others, the desire to procreate has already been satisfied, or is already compromised by other factors, such as a vasectomy, vow of chastity, sexual orientation, or erectile dysfunction. If the victim has already made peace with not having children in the future, it is possible that a treatment which had this side effect wouldn't be such a bad thing. However, depression is a wily foe, and it's not unheard for someone that has had a vasectomy, for example, to be suddenly hit by a wave of depression upon hearing that their depression medication is rendering them infertile. Such is the insidious power of this disease, which is why it can never be treated as if it were a merely physical disease.