This report from the Open Society finds that addiction treatment reduces overal health care costs. 

From the executive summary:

Addiction is a pervasive yet treatable chronic health condition. Often it occurs alongside other chronic diseases.  If untreated, the addicted person's medical care becomes more costly due to secondary health conditions.  When treated, addiction leads to better health care outcomes. This paper demonstrates how addiction treatment will contribute to containing costs in reforming America's health system.  Studies show that addiction treatment significantly reduces emergency room, inpatient and total health care costs.

Open Society Institute. (2009). Unforeseen benefits: addiction treatment reduces health care costs.