To expand on the answer I gave, Bound Man was swiftly ouclassing Doflamingo. His awakening could buy him some time through keeping Luffy away from him, but a Leo Bazooka was already enough for Luffy to nearly finish him. Whilst Doffy was weakened before battling Bound Man, Luffy wasn't on his prime condition either as noticed by Doffy, plus the lack of a statement from someone informing us the outcome would be any different had Doffy been at full power implies the injury wasn't too much of a hamper fact on Doffy's performance imo. Meanwhile, bound man was no match for Katakuri, with him only getting hit when he lost his concentration and couldn't use his observation haki to its fullest... besides it, his defense with his mochi power was already enough to negate one of Luffy's most powerful attacks on Bound Man and he still had strength enough to stalemate a state who is faster and, consequently, stronger than the boundman, letting Luffy with barely any energy left post fight.
Doflamingo's only chance would be trying to make Katakuri lose his focus and then attacking him with a letal technique, but even that is doubtful in succeeding as Luffy's strongest attack in bound man was enough to shatter through Doflamingo's God Itto.