Are we beating this old horse again??
Mark, you've gotten some pretty good answers already but maybe not in depth enough to truely answer your OP.
I'll try to be as simple and brief as possible(

).
Someone has already told you that true depression is a PHYSICAL illness. Perhaps though you need to understand why it is a physical rather than a spiritual issue.
I'm going to start by making a comparison to a very different illness. Diabetes is caused by the body being unable to to produce the chemicals it needs to process the sugars in our diets. There are different forms of diabetes, but the end result is the same: sugar builds up in the blood and will kill you if you don't do something about it.
So for some people, simply watching the amount of sugar they eat every day and exercising more, will control the build up of sugar. Others take a daily medication(chemical) to further help the body process the sugar. Still other depend on insulin injections. Insulin is a chemical produced by the body. Let me tell you what happens if you don't have enough of it.
You find yourself so sleepy that it is impossible to function. It makes you feel very thiristy(whether or not you really need more water in your body). If you don't heed the warning signs, it'll lead to various other symptoms including hallucintions.
http://www.diabetes.com/blood_sugar.html
Now a persons body also produces various chemicals that allow the brain to function in the way we consider normal. Normalcy includes being able to communicate, feel our body parts, be able to tell when we are tired or not, hungry or not, takes what our eyes see and ears hear and turn it into information that ours brains can use to allow us to function during a normal day. Most of the time we don't even know these processes are going on. God created an amazing body for us that is sooo complicated and has so many different processes going on all at one time that man may never fully understand it.
We do begin to understand pieces of it, when something doesn't work properly. Back to those chemicals the body produces. Insulin isn't even produced in the brain, the pancreas regulates it. But without it the brain won't function properly and when it misfunctions in this case it is going to cause a person to hear and see things that aren't there.
Is this a symptom of a SPIRITUAL nature? Most of us would agree that it is not, that the physical basis it the diabetes. Introduce and outside source of insulin and the hallucinations go away. Does that make insulin a mind altering substance? I'll let you answer that one yourself.
Now, what if you body stops producing this little chemical called serotonin(
http://www.medterms.com/script/main/art.asp?articlekey=5468 )? Or if it produces to much? Or if the amount it produces fluctuates from one time period to the next?
You are going to get symptoms just like you would if you were diabetic.
Is there a physical basis for those symptoms? Absolutely. Add a medication that adjusts or controls the amount of serotonin and the symptoms are relieved. Are these medications mind altering? Some of them are mind altering in the same way that insulin can alter the hallucinations. Some are even more so and the wrong medication can make the symptoms worse. Thats why medications should only be taken with the advice of a competent physician. If you take to much insulin or you take it the wrong way, you end up with another whole set of problems.
Now we've talked about the PHYSICAL side of both problems. Now it is time to deal with the SPIRITUAL side of both issues.
If you are diabetic, you quickly learn that the first course of action is not medication! The first course is to adjust that diet and get some exercise. In a good portion of diabetics this alone will take care of the problem. But what happens if the person won't make those adjustments? Is that a physical problem or a spiritual one? You know where I'm going, at this point the physical problem becomes a spiritual one.
Now if you're suffering from depression, there are also certain steps outside of medication that you can take at the beginning. Because our minds and our thoughts can affect our bodies production of serotonin, sometimes it is possible to alter the brain's "diet", without medication. The brain's diet is a lot harder to adjust, let me tell you. And I think this is where the confusion between what is basically a physical problem becomes confused with the spiritual.
We have so much information coming into our brains, that it is very hard to pinpoint exactly where and with what information the symptoms relate to. This one little chemical called serotonin controls sooooo much.
It is possible for a person to adjust the stimuli that they are exposed to and that adjustment may allow the body to better regulate the chemicals that make us work. In the case of diabetes, we can control the sugar. In the case of depression, it may be that we can control the stresses of our daily lives. With the brain the answer is different for everyone.
If in either case we are not willing to make the adjustments, then we have a spiritual problem. The Bible says that our bodies are the temples of the Holy Spirit. If we believe that than we should treat it as such. We should keep it in the proper order so that it can work for the glory of God.
The spiritual problem in both case is not mind altering chemicals. The problem is, are we doing our best in regards to our bodies to provide the Spirit a temple?
Now back to outside stimuli causing physical problems. Just like no exercise, being overweight and eating to much sugar can lead to diabetes(a physical problem), so can genetics, stress, abuse, sin and even the food we eat lead to depression(also a physical problem).
Now to finally answer the OP, not only can you have God's peace as a diabetic, you can have it as depressive. As a sufferer of depression myself, I know I wouldn't have made it through without both the Lord's strength and peace AND my medication. I couldn't move during the worst periods of depression. I wasn't particularlly sad, but it made me angry if someone wanted to talk to me. I just wanted to be left alone to vegetate. I wasn't involved in any overt sin(ten commandments stuff), didn't even have time for that as I had a 2 year old and a newborn. I was just tired in my bones. Not the good, I've done a good days work tired, but a drained out, no strength kind of tired that didn't go away no matter how much I rested. This isn't and wasn't normal for me. I almost always have something going on and I talk practically constantly, to the point that my family kids me about the phone growing out of my ear! Reading my Bible and praying gave me peace, but didn't relieve my physical symptoms. It took medication to do that.
Below is a link to a very good but long article on depression and it's causes.
http://www.medicinenet.com/depression/page2.htm
Hope this helps answer your question.