"Not necessarily...
In fact, late in the film, Obi-Wan may even mention that Dooku was right all along...

"But I would assume that Obi-Wan would still believe that Dooku was fooled, much like Anakin. I mean, we don't want to comprimise Obi Wan's moral standing here."

Regardless of what Obi-wan mentioned or believed, Dooku was Palpatine's apprentice, and he even called him "Darth Tyrannus" at the end of AOTC. Being raised from birth as a Sith, or being tricked out of the Jedi order doesn't change that fact at all. Sith manipulate everyone - even other Sith. That doesn't change their relationship. If fact, it defines it.

"One of the themes throughout the films is that the Sith lords, when they started out thousands of years ago, embraced the dark side. They were greedy and self-centered and they all wanted to take over, so they killed each other. Eventually, there was only one left, and that one took on an apprentice. And for thousands of years, the master would teach the apprentice, the master would die, the apprentice would then teach another apprentice, become the master, and so on. But there could never be any more than two of them, because if there were, they would try to get rid of the leader, which is exactly what Vader was trying to do, and that's exactly what the Emperor was trying to do. The Emperor was trying to get rid of Vader, and Vader was trying to get rid of the Emperor. And that is the antithesis of a symbiotic relationship, in which if you do that, you become cancer, and you eventually kill the host, and everything dies." - Bill Moyers Interview Lucas: Ex-Jedi Dooku - later revealed to be a Sith Lord, Darth Tyranus - not only served as the movie's principal antagonist, but was also a means for Lucas to illustrate a number of important story points. "I needed to get across the point that Jedi can leave the Order," Lucas explained, "to set up what happens with Anakin later on. Also, in the end, when you realize that Dooku is Darth Tyranus, it explains what Darth Sidious did after Darth Maul was killed: he seduced a Jedi who had become disenchanted with the Republic. He preyed on that disenchantment and converted him to the Dark Side, which is also a setup for what happens to Anakin. - Mythmaking: Behind the Scenes of Attack of the Clones