It wasn't necessarily a question of more effectiveness, as of changing the tactics. Up till that point, Anakin was about to lose due to expending more Force energy than Dooku. 2-bladed fight would change Anakin's pattern and thus force Dooku to change his pattern.
Also, it's clear that this wasn't some deep-thought stratagem by Obi-Wan. It was a spur of the moment, desperation-inspired Hail Mary pass.
“Unusual,” Dooku said again. “But not enough to save you this time!” He came on hard, thinking to drive Anakin back and off balance as he
had driven Obi-Wan back. But Anakin held his ground stubbornly, his
green blade flashing left, right, and down so forcefully and precisely
that none of Dooku’s attacks got through.
Off to the side, Obi-Wan understood that it couldn’t hold. Anakin was
expending many times the energy of the efficient Dooku, and as soon as
he tired …
Obi-Wan knew that he had to do something. He tried to come forward,
but winced and fell back, in too much pain. As he collected his
thoughts, he reached out with the Force instead, grabbing at his
lightsaber and pulling it in to his grasp. “Anakin!” he called, and he
tossed the young Padawan the blade. Anakin caught it without ever
breaking the flow of his fighting, turning it under and igniting it
immediately, putting it into the swirling flow.
Obi-Wan watched in admiration as Anakin worked the two blades in
perfect harmony, spinning them over and about with blinding speed and
(R.A. Salvatore's AotC novelization)
Clearly, that didn't quite work as expected, as Dooku adjusted easily and shortly, dis-dual-lightsabered Anakin:
And he watched with similar feelings the working of Count Dooku’s red lightsaber, flashing ahead and back with equal precision, picking off attack after attack and even countering once or twice to interrupt the flow of Anakin’s barrage.
Obi-Wan’s heart leapt in hope as Anakin charged forward suddenly, bringing his green blade over his shoulder and across, down at the Count. Obi-Wan understood immediately, even before he noted Anakin’s blue blade coming up and over the other way—the green blade would push the Count’s lightsaber out of the way, clearing the path for the victorious strike!
But Dooku retracted impossibly fast, and Anakin’s down-cutting green blade hit nothing but air.