Yes, due to the compression of spiritual pressure. It's not because of the bankai's power that it gives him speed. This means that while yes, his natural speed can improve, but it doesn't increase his stats or boost his speed, the condensation effect produces said effect. It doesn't give him enhanced reflexes, He already has those reflexes normally, he can just dodge it better and move quicker. Do you want me to tell you why it's not his power. The biggest fatal flaw about his ability that makes it not his own power?
The simple fact that the
extreme speed effect doesn't naturally grow accustom to his body. So I'll explain what that means.
It means that thanks to the special trait of condensation, and thus less spiritual pressure it's of a similar effect to
Aang's ability to increase his speed by decreasing the air resistance around him. Thus it increases his speed, but it doesn't "cushion" the amount of force that's generated in his movements so he's still capable of massively breaking every bone in his body through overuse. So you can't use that multiplier effect just because it's decreasing the spiritual density around him, you can't ten times an effect that's not his own effect. The False Bankai's true ability is only producing stronger Getsuga Tensho, a Bankai isn't supposed to hampen a characters ability to use it unless it has to do with their overall reserves.