jakebohall - 3:27 pm on May 23, 2013 (gmt 0)
In my experience in working with companies using this tactic with template and widget bait, it can go either way. In many instances the links were mostly devalued and the impacts were negligible.
This could be your case due to the fact these are sitewide and easily algorithmically identifiable as Martinibuster pointed out... and we are talking about a single domain.
Since it sounds like this change is inevitable, I would suggest focusing your effort on finding a few authority links to replace the one you will be losing. I'm looking forward to hearing how it plays out for you.