Maybe. There a lot of instances where Doflamingo could have used Parasite against Luffy and Law but didn't. Perhaps a certain amount of Haki is required to use the ability, but that implies Jozu is inferior to G4 Luffy and Law...
Just seems like an inconsistency. Perhaps Luffy could only break the strings because his body expanded so much. Doflamingo was shocked that he was able to after all. The fact of the matter is that Jozu held his own against an Admiral and Whitebeard trusted him to do so. Doflamingo wanted nothing to do with Aokiji when it came down to it.