Good lord - I'm so glad you're still here, harlans. At this point, I think you must face the fact that whether or not you keep your employment is an issue that truly would not matter much if you had been successful.
If you're that worried over it, I would recommend checking with a lawyer first, but one thing's for sure - being an alcoholic is not grounds for termination. If you had come into work too intoxicated to perform your job (or intoxicated at all, for that matter), that would be a different discussion I am sure. But generally speaking, if a person is going through alcoholism/drug addiction concurrent with active suicidal intent and plan, your employer may already be aware of it. One of my closest friends told his employer about his alcoholism before he checked into rehab. His employer told him that he was so happy to hear it because, though my friend was (and is) one of his best employees, he was about to be terminated for poor job performance which his employer could tell was the result of either a psychiatric or chemical dependency issue. My friend is now 1.5 years sober and has the best relationship he could imagine with his boss - They have a mutual respect now that could only have been fostered under the conditions of self-disclosure and honesty.
~ Vaya
Edit: My HR department has plenty of health and wellness initiatives they offer to their employees who are coping with psychological and/or addiction distress, and as long as you express an earnest desire to get clean, they ought to work with you - should they offer such programs. Check with your HR department.