Yes. Mania is a physical problem.
And, since the question is [important], there is a little more we can say.
Some people are prone to mania and some are not. Those who are prone to it are neurologically different from those who are not, even though there is little or no scientific evidence for those differences yet. The reason we can say it is physical is that it is not spiritual. That is, the spiritual is expressed in those behaviors and thoughts that are either commanded or prohibited by Scripture. Mania is neither commanded nor prohibited. It is physical by default like pneumonia or cancer.
We are embodied souls—physical and spiritual. Some behaviors call attention to the spiritual while other behaviors highlight the effect of our physical bodies. When someone is violently angry, we are not too concerned about brain function because the problem is definitely spiritual. But when someone is blind or lame or even having an incredibly difficult time with math, the problem is physical. Likewise, when someone has emotions that are excited and elevated for no apparent reason (i.e. mania), and those emotions stay at that level no matter how much the person would like them to come down, the problem is physical.
Where this gets tricky
Where this gets tricky is when those who are manic commit flagrant sin, especially sin that they might not commit when their emotions are in a normal range. This is so common that behaviors such as “sexual indiscretions” are mentioned in the diagnostic criteria for mania.
These sins, of course, are spiritual. To say otherwise would create one of the most frightening scenarios we could imagine.
“I, Ed, take you, Sharon to be my wife. I promise my fidelity to you, unless I have some brain-thing happening that makes me have sex with someone else or makes me dump every penny we have on a lottery ticket.”
Is it possible that the body can make us more vulnerable to temptations? Absolutely.
Anyone who has ever been cranky because of little food, little sleep or PMS reminds us that the body can be a stumbling block. But those same people confess their crankiness rather than blame it on their bodies.
God can sanctify
There are ways that mania creates intense and unique temptations for people, and I think that many of us would not do well in the midst of those temptations. When you begin to understand mania you become more patient with those who experience it. But we know this: the Spirit of God can sanctify manic people even if their mania persists.