If maul wasn't sliced in half by Kenobi would Sidious still have recruited Dooku?

Hi if Darth Maul had not been sliced in half by Kenobi during their duel on Naboo would Sidious still have recruited Dooku?

and would there have been a rule of three with Sidious as the Master and playing the role of the Chancellor Palpatine, Darth Tyrannus as the leader of the separatists due to his former Jedi past and being the Count of Serenno, and Maul in the role of Grievous or running the Shadow Collective for the purposes of the Sith?

https://preview.redd.it/dwm2w5o6ohfg1.png?width=1200&format=png&auto=webp&s=c2c03c42d4369bcf40e5231c9d28ace6f13a90d4