I have no experience of loved ones in jail nor an addicted child.
But my son did have severe major depressive illness in his 20's which absolutely required serious medicine combined with therapy. Without the medicine--a combination of antidepressants prescribed by a very experienced psychiatrist who also counseled him once a week-- I am not sure he would have survived the mental anguish. Depression is a medical condition, it is an organic disease of the brain, and in my opinion, when it is debilitating should never be left just to "level out." It destroys brain tissue and damages bodily organs and lasts for years.
If the jail offers medical treatment, as I assume it does, I would intervene enough to get your son treated for medical depression. In his state of mind, he will not be able to advocate for that. And he is very young.
Depression can take two to three years to completely resolve. If he is put on medication, it may be a few or several months of adjusting the medicines and dosages. And in fact he may require antidepressants for many years. Anti-depressants also relieve the accompanying anxiety depression creates.
I personally would have little hope your son would get well in jail unless he is treated for both addiction and depression. If you bail him out today, there is little chance he will stay in rehab or clean long enough to allow any anti-depressants to take hold and level out the skewed brain chemistry.
If he is in jail for up to a year, however, and receiving medical treatment by a qualified physician, maybe it would give him a chance to gain some ground mentally and be stable enough to do recovery work.
I could not cure my son's major depression, but I could and did spend thousands of dollars on medical treatment that did make him well. Major Depression cripples the sufferer, and family intervention is necessary. I know my experience is not a parallel to yours, as yours is complicated by your son's addictive disease. But I just needed to say that if your son indeed is suffering with major depression, he should receive treatment for that.