if the keyword phrase is 'green widgets' and you get a large number of links with anchor 'green something' (but no 'widget' in the anchor) and a large number of links with 'something widget' (but no 'green' in the anchor), will you rank for 'green widgets'?
I might help, but it won't help as much as getting links for the term "green widgets". What I'd do is get most of my links for "green widgets", then spread about 20-30% of my other backlinks for "green something" and "something widget".
We tried it, that's the reason we could say this to you else we might have asked you to try it and let us know the result