Brief Answer:
Pretty much unquestionably

Detailed Answer:
It's primarily folic acid and thiamine.
First, it matters a lot what the rest of the nutritional context is. If someone is otherwise not getting b vitamins, or losing them (serious illness, caffeine, cancer, trauma, a lot of glucose intake) then, sensitivity to alcohol will increase.

Second alcohol interferes with uptake of thiamine AND increased metabolism of carbs like alcohol is associated with INCREASED thiamine NEED. This probably extends past the period during alcohol intake, but I haven't seen how long it goes for. The very high risk of symptomatic deficiency disease in alcoholics (certainly over 10%) makes one think the effect on thiamine is pretty big.

The biggest category of increased thiamine need is alcohol withdrawal which frequently precipitates thiamine deficiency disease.
http://www.ncbi.nlm.nih.gov/pubmed/0000 (many, many other examples).
If you've ever had serious withdrawal symptoms, you've been at risk. Indeed many researchers wonder how much of the withdrawal symptoms are due to thiamine deficiency.

BUT, just take the vitamins and the deficiency goes away. The current recommendations are HIGHER THIAMINE and FOLATE amounts per day than what is usually in a once-a=day vitamin (100 mg and 1 mg respectively). But the one a day is not far from the prescription dose.

I hope I have answered your question ("yes").

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Brief Answer:
depends if it can reverse!

Detailed Answer:
changes in nails are usually reversible. This can be from vitamins (a LOT of them are implicated and vitamin A, D and E are not directly affected by alcohol.... BUT if you aren't eating properly.. then they will be affected. The simple cheap store brand one a day covers all of these Well!)
It can be from iron deficiency.... You will want to have that tested for. Iron deficiency is often from bleeding. Alcohol, being a solvent, irritates the stomach lining and causes bleeding. Can be slight over a very very long time and cause really bad anemia. Fixable.
It can be from protein malnutrition. It would be noticeable. It can be from liver disease and at the level for nails to be affected.. which does not take fatal liver dysfunction... it might be very hard to tell how bad the liver is... 50% gone or 75% gone is hard to tell from not bad at all. Good side is that there's very little problem from 50% liver disease bad side is you can't necessarily tell if you're headed downward til you're at 70-90% cirrhosis.
But
The grey hair... I'm not sure that can be reversed.

Nails grow really slowly. It takes 3-4 months for them to grow out. (ask about any female they will have really good estimates).

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Brief Answer:
I've never ever seen that get better. Baldness

Detailed Answer:
especially in women. Heck it's getting better in me (with a lot of rogaine). but other than dyes I'm just not seeing people become not grey.

It's bunk.
http://www.ncbi.nlm.nih.gov/pubmed/0000

Maybe if you look out the window enough times you see 2 red cars next to each other showing your special abilities ! (well, it's a chance occurrance and they looked a lot of times in this study to see anything; most studies are not finding anything). FURTHERMORE, They do NOT see a REVERSAL in grey.

FIFthermore (I'm up to about 5) if grey were reversed. You'd see LINES of color in hair the way you do with dyes. you DO see lines in fingernail growth and fingernail fungus recovery.
http://www.medicalopedia.org/1796/white-lines-on-nail/ like these!
which can be due to zinc. BUT as the article mentions it is more commonly seen with nutritional state (like tree rings... trees grow in spring, they don't grow in winter; and, the rings are bigger in good years smaller in droughts/etc). AND alcohol can be associated with bad nutrition and periodic phases in drinking WILL do this to nails.

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