Very subjective question. Majority say you'll have a bad trip, it'll be a nightmare, you might kill yourself, etc. But I had my first trip when I was suicidal depressed. I was stuck in this loop of wanting to end it all for what seemed like hours, then it was over, and I felt as though I appreciated life, I loved myself, energy was all around me. I was transformed. It took the right setting though. You have to be able to work inwards without being interrupted, and "friends" often don't let that happen and want to make your trip all about themselves, especially if they're inexperienced with psychedelics. You have to have a setting where you can't throw yourself out the window, or otherwise use a short impulse driven action to end your life. This means no stove access, no fire setting, no windows to jump out of, a safe setting. Yes, it will be a "bad trip", but if you're depressed you're already in a bad mental state, psychedelics will amplify that. You will have the power to transform your emotions far better under psychedelics though, and lots of research is being done into magic mushrooms and other psychedelics for therapy for mental illnesses.
What's important about your question is WHICH psychedelic you decide on, as well. A small dose of magic mushrooms is what I recommend starting with. By small I mean very small, make it an introspective trip, look inwards, and avoid going outside or interacting with others for the first few hours of your trip.
To me, psychedelics aren't just about "being happy". The human mind is complex, this complexity is what gives us the full experience. Read Aldous Huxley's "Brave New World" if you want to know what a society with no other emotion is. In order to get the full psychedelic experience, you must dose even when you're not in the brightest of days. It will be intense, you will cry, you may get suicidal, but the takeaway is that you will get an insight into your mind.