Not likely, would be my answer. If the methodology resembles what the magazine controversially publishes about law school rankings, general counsel won’t learn much that they don’t already know. The name brand firms will strut through the top 25, the factors that go into the rankings will be criticized (size, profit per partner, citations in publications), the weightings given them will be questioned (what about diversity??), ads and RFPs will brag, and big reputations will get bigger. Even the subsequent years of the rankings, where rises and falls in rankings will be invested with deep significance, will fail to impress the market.
In fine, the rankings will generate discussion and disputation far out of proportion to their effect on general counsel.