Short answer no

Longer answer - in a hypothetical universe with just the sun and the two planets maybe. Planet B can rest at the L2 Lagrange point. However it is unstable, so any slight perturbation, no matter how small, would push the planet off that point.

In our real universe these perturbations happen all over the place. Even if you have an isolated three body system, tiny gravitational influences from distant stars is enough to destabilitize planet B from L2.