Funny I was thinking about that not too long ago. I discounted it for a couple reasons, but I thought one thing that might trigger a strike would be that when the weight hits the bottom, the line goes limp and the jig comes to a more natural stop. More natural than say jigging when it comes to an abrupt stop.
To me it seems like more hassle than it is worth, but I might try it if the bite is slow and I get bored.
When I do, I think I am going with a tiny plain hook with as little weight possible. Fishing with a weighted ice fly would seem to defeat the purpose.