Are you talking about using pivot English? It's hard to follow.
Speaking generally about all types of english, it actually depends on how much elevation you're talking about and where you're hitting. Hitting top with sidespin and an elevated cue will make the CB swerve more initially because the CB is being pushed into the cloth to start with, digging in and propelling itself in the direction of its spin. Hitting with low sidespin regardless of cue elevation, you're generally hitting a bit harder to get the CB there before draw wears off, but the CB will swerve, curving after it's traveled a bit. You use an purposely elevated cue less when hitting low on the ball, but if you do use an elevated cue and hit near the miscue limit, you'll get a semi-masse where the CB curve comes in late.
Short of it is, a CB will curve more at the start with a top CB hit, and the curve will be a little delayed with bottom, but I don't know that one actually curves less, speed being equal. It's just you typically hit bottom with a bit more force so the CB gets where it's going before you see the full curve of the ball show up, but the CB will curve.
And it's absolutely untrue that a level cue will result in no CB curve.. A level cue will delay the transfer of sidespin to the cloth and the onset of the curve, especially with firmer hits but its an inescapable conclusion of physics that the ball will curve unless its rotation is the same as its direction of travel. Even if you had magic frictionless cloth, the spinning ball would still curve just because of how a spinning body alters airflow over its surface. See: Magnus effect.