The answer might technically be "no" but why risk it? Where is the line between "depression" and "clinically depressed to where you might be a threat to yourself or others"? I think it's a very fine line, that you would probably have to go to court to have determined.
Say you see the doc for depression, get a prescription, while paying for your prescription you appear nervous and your CCW, gun permit, or some other telling sign you own guns falls out of your wallet. Depending on which area you live in, don't some states still have the narc on your neighbor if they guns programs, you might be getting a visit from the local PD who will want to hold on to your firearms until you are "better".
In today's world this is a possibility.
Now if you are depressed, to the point where you need to see a doctor, then I say it becomes questionable about having firearms at your immediate access. Let's face it, it's not the happy people who have everything to live for that take themselves out, it's the people who are depressed.
One of my mom's friends is bi-polar and very depressed about it. She was on suicide watch before Christmas and then seemed to be better. Then last week she tried to kill her self by taking an overdose on pills.