It goes back further than Cherington when it comes to free agent signings. Brian MacPherson had a tweet thread today where he pointed out that since 2008, the Red Sox have signed 16 players to multi-year free agent contracts and only two of them have finished their deals in a Red Sox uniform: Chris Young and David Ross. All the rest, except David Price and this year's signees who are obviously still playing, were dealt or cut before their contract expired. Among those being Hanley, Sandoval, Dempster, Gomes, Victorino, Crawford, Lackey, Cameron, and Scutaro.
The last free agent player signed by the Red Sox to a contract of more than two years who played out the whole thing in Boston: JD Drew.
Free agency hasn't worked well for the Sox for years, dating back to before Ben Cherington. Maybe it's not entirely on him.