Depends on the drug class, because there are a few types of antidepressants.
When it comes to SSRIs (the most common class), fatal overdose is technically possible but happens rarely. Basically even if you take a huge dose there's still a big chance you will survive, just feel very sick. Google serotonin syndrome. That's what can happen to you. Though most of the time it will not lead to death, just a long time of worse torture.
For other drug classes, I haven't researched it much but as far as I know the answer is similar. Tricyclics can be more fatal, in general, but still quite unlikely to cause death.
Short anwer: you would have to be extremely lucky to fatally overdose on antidepressants, and even if you did, you would probably die living throguh a horror. Not really worth it.