Of course your doctor is the one to talk with...
I will however say that for a long time, even before I became an alcoholic and still to this day (sober since Dec. 6 2011) I take a daily multi-vitamin.
It wasn't so much to do with drinking but to fill the gaps because as a teenager, college student while working full time, now father who still works full time my busy life means I don't always eat the healthiest of meals so I felt it helped with some level of general health.
If you've done the blood work with your doctor and some vitamin levels came back deficient but your doctor didn't seem to worry then I wouldn't either. However, if you're like me and still worry then simply ask him what to do, he'll likely recommend a simple over the counter, one a day mens multi-vitamin.