There isn't any reason why Mace Windu would not be able to utilize Vaapad as he did against Sidious. Sidious > the Count. However, in the novel, it is suggested that Mace had never been so submerged in Vaapad before, which could be an indication that any state close the one he was during his fight against the Sith Lord was of very rare occurrence.
Except Mace's boost only makes him equal to the combatant he is facing. And since he and Dooku are so damned even the boost he'd get from Vaapad is minimal. Also for decades Sidious wasn't just a master of the Dark Side, but he was an embodiment of the Dark Side himself. So naturally Vaapad would give Windu an unimaginable boost. This is the guy who with Plagueis waged war against the Force itself and tilted it into the Darkness.
Sidious was THE avatar of the Dark. Dooku in comparison is a master of the Dark Side.
It doesn't just make him equal to the foe he's facing it also gives him MUCH more stamina as he's constantly feeding off the dark energies of his foe.. while the opponent isn't and will get tired sooner. So it gives him a clear advantage and this isn't even including shatterpoint.
What you describe is exactly what we see in the duel between messieurs Windu and Sidious, indeed, I believe the latter made a number of comments along the lines of, "I'm too weak".
But then - and I could be wrong here, so please do correct me - the Chancellor screams out "unlimited power[!]" and proceeds to blast his opponent out of the window.
Furthermore, the novel explicitly mentions Windu's fatigue:
"'You're the chosen one, Anakin,' Mace said, his voice going thin with strain. This was beyond Vaapad; he had no strength left to fight against his own blade."
Rather a gaping flaw in your theory, one would think.
That isn't a gapping hole... Vaapad giving mace more stamina doesn't contradict Mace almost being overwhelmed by Sids lighting. Those things aren't mutually inclusive. That's like saying.. a boxer was clearly tired because he was struggling to stay standing after gettnig hit with bombs.. no.. it had nothing to do with Stamina and all to dowin with the powerful punches he was taking. Same thing here... Sids powerful lighting was making Mace work and struggle a lot not to be taken out by it... That has very little to do with stamina. The same novel you quote mentions how the Mace is constantly feeding of the energies of the emperor to replenish his energies.
What does the emperor saying he's too weak to continue and not being too weak to continue have to do with this discussion. I don't remember ever saying the emperor didn't have something left.. we're told he did by Lucas himself. That though, again, has nothing to do with Mace increasing his stats including stamina and speed through the energies of a DSider