I really don't know. 
 
Let me provide some additional context around your question. 
 
Are you talking about the Church itself as an employer - or Mormons in general as employers? If you are talking about the latter I doubt that Mormons would take that kind of stance against one of their employees or one of their employees dependents. There might be a small minority, but Mormons in general try to be understanding and accepting of others life choices. 
 
If you are talking about the Church itself as an employer - then that requires a different type of discussion. Just so you know - the Church has a lay ministry and therefore the number of paid employees the church has would be relatively small. Obviously the vast majority of paid employees of the Church live in the Salt Lake City area and work at Church headquarters. There are some paid Church employees around the world (facilities, teachers in the Church's institute and seminary programs, welfare program support employees, etc.) Whenever anyone works for the Church they agree to be "Temple Recommend" Worthy. This means they agree to not smoke, drink, have marital affairs, steal, pay a church tithing, etc. If the employees make a mistake - the Church in most cases works with them to repent and correct their mistakes. If they choose to continue to be out of accord with the agreements they made when first hired by the church they cannot continue to work for the Church. 
 
With that as background - (and I am guessing with this) - that the Church would help pay for abuse treatment (all dependent on what the abuse was). Also in the case where the employee was ok, but one of his dependents had some abuse problem I would guess that the Church would cover that. But that is all just speculation on my part. I don't work for the church so I am just going on what I have seen and heard from others experiences. 
 
One other thing: The Church is generally a very fair employer. In the past they have tended to pay a bit under the average wage given the great demand among Mormons to work for the Church. However, I have heard that the Church has upgraded their pay to be more on par with similar jobs with other companies. Also - the Church offers very generous benefits to include excellent medical coverage. They provide some level of matching for 401K funds and they also continue to provide a pension - which as you know is getting to be less and less common. Additionally at the Church's universities - BYU, BYU-Idaho, BYU-Hawaii, and LDS Business College - the Church provides subsidized tuition (I have heard upwards of 70% for each student) and is very, very aggressive in providing employment and earning opportunities for students to help them earn their way through school. 
 
ps Opinions expressed on AskaMormon.com are solely the authors. The Church neither supports, endorses nor sustains anything on AskaMormon.com

LDS employers follow State and Federal Labor Law when it comes to benefits offered to employees. An LDS owner of a business is no different than any other owner of a business.  
 
Now the LDS Church is a Self Insurer and I do not doubt that they have refuse to allow the tithes that fund there healthcare packages to go towards some medical operations like an elective abortion, asex change operation, or provide coverage to a same sex partner. To do so would violate the highest trust of the membership and the highest tenants of the faith, and no Governement has the right to impose regulation on the expenditure of tithing monies, even in the name of "healthcare reform".  
 
Now the LDS Church has only a very limited amount of employees, and a requirement for all employment in the Church is active membership. So in reality while I am sure they have legal documentation to protect them from ObamaCare, the employees of the Church are members of the Church and would not be getting elective abortions or sex change operations or having a same sex partner etc.  
 
As far as detox, the Church incourages those who are addicted to any substance to get help to overcome the physical, emotional, and spiritual enslavement of addiction. I would never see the Church trying to stop someone from seeking treatment for addiction.