No Dooku was a pawn in sidious game the entire clone wars was a distraction from the development of the Death Star which unknowingly to both sides was funded by each other. Sidious had Dooku seek out Jango Fett and created the clone army for the Republic and created a separatist movement to find all potiential traitors ahead of time. By creating a fake enemy and painting the Jedi to the public as war monger Sidious was able to convince the Senate that a government with one body holding all power can’t be easily affected by defectors. Count Dooku was old and he needed a younger apprentice to enforce his new empire also Dooku was already painted as villain so he had to kill him.