Probably not. Although whatever caused that might still be on the coin and could further create more of that corrosion appearance. Best bet would be to dip it in Acetone and then distilled water.
It is odd that most Silver problems are simply from Oxydation or Nitrates but so far I don't think anyone really knows what causes the so called milky staining. If yours is as you said, crusty and dark, sounds like some sort of Nitrate and the Acetone should stop any further problems. The main thing is with Silver is what your mentioning is already into the Silver of the coin and even if somehow removed, part of the Silver will be lost too. Usually removing such corrosions leave actual holes where it was.
Now you'll have to rememver not to turn the page and look at the reverses though.