Well, hardly. He left the Jedi because the Senate was corrupt or something... We can sort of make out that he left Jedi order because it's under the inlfuence of a Sith Lord (and we still don't know exactly what that means, other than some evil guy). What exactly that has to do with his position in the Jedi Order (which we know from the novel was a fairly esteemed position) is not clear either...
He's clearly playing a game, pretending not to belong to Sidious, but to lead the Separatist movement... So we have to conclude that Dooku suggests he left the Jedi order because it's corrupt and led by a Sith and decided to join the 'good' separatists... He even suggests QGJ would have joined, even though QGJ battled the TF (part of the separatist movement) as bad guys in TPM... yeah, right. Very credible not...
But we don't learn anything from Dooku's real motivations because he belongs to Sidious. He just delivered a cleverly constructed story. We find out at the end of AOTC that he is Sidious' new apprentice and that he is the one planning the war for Sidious.
So why did he leave the Jedi Order?? Because the Senate was under the influence of the Sith Lord he decided to serve???? That doesn't make sense other than it being a fake story to OB1. Ergo, we know nothing still.