Will I be denied or fail a first class medical if I have a recent history of depression?
According to 67.107 which is the guideline for AME's for mental issues, depression is not listed as a reason for automatic denial for first-class medical certificates.

The issue with depression comes in when you are on medication to control it, as many antidepressants are considered "do not fly". It isn't impossible though even with medication and treatment, the FAA has published a guideline for AME's about antidepressants and treatement, and the granting of special issuance medicals.

What you do not want to do is to lie about it on your application, as falsifying your medical history is grounds for revocation. Getting your medical reinstated after lying about your prior conditions is very difficult (and expensive).