jclan:
I do not think he is a "poor" employee but I feel I need to do something to turn this behavior around.
Which behavior are you talking about? The drinking or the being sick? Here are some things to think about...
Have you investigated the employee for alcohol levels at work? Do you have a drug policy that includes alcohol and stipulates the Company's right to test in reasonable suspicion situations? If so, why have you not done that? If not, what have you done to correct that?
Does your Company have FMLA requirements? Does it have them in some places and not in others? Do you know the status of the employee's potential to be qualified for FMLA coverage if the Company is burdened by FMLA compliance requirements?
Team morale is the team leader's problem, not yours. Make sure the team leader is informed and be available to help him or her. As soon as people start talking about being offended over such twaddle (how does the complainer know he was the alleged source of the plague?), I start talking about growing up. This isn't just one guy being sick and another guy being offended that he was reportedly the source of the disease. This is about two people behaving in a silly manner that is distracting from the purpose of their employment and a burden on HR resources and it should be nipped in the bud rather than fostered.
How do you know the episodes of calling in sick or due to anything other than sicknesss? Medical notes won't tell you much these days because the doctor's now pretty much say "so and so is under my care and is approved to return to work on <date>" and they don't have to tell you anything more and often can't. You won't get, and you are not entitled to, medical information unless this is an ADA fitness issue or a FMLA cert situation. Beware improper medical inquiry under ADA.