While their utility in their originally-intended role (fighter) would be short-lived if not questionable altogether in face of purposely-designed high speed all-jet aircraft, I was reminded of something else......
In WWII, particularly after Japan started its string of defeats in the Pacific, Japanese D4Y Suisei dive bombers began to be outfitted with rocket booster bottles to help with two types of things- first, takeoffs with heavy loadouts, and second, terminal dives on targets (a.k.a. Shimpu a.k.a. Kamikaze).
Now neither of the two would be all that meaningful to the Americans, but if, say, the Fireball and Dark Shark are to be employed as fighterbombers (with more emphasis placed on the second part of the term), would having a jet booster help in attack missions of conventional nature?