Is the hydrogen atom attached to the benzylic carbon in benzaldehyde acidic?
Yes and no.

What you discuss is only possible if the $\ce{C-H}$ bond is perpendicular to the ring plane. However, since the carbonyl group is planar and better conjugation can be achieved with the $\ce{C=O}$ bond participating in resonance with the benzene ring the predominant configuration of unsubstituted benzaldehyde should be planar, i.e. the $\ce{C-H}$ bond being in the ring plane.

If you introduce steric hindrance, e.g. 2,6-di-tert-butylbenzaldehyde, the chance of the carbonyl group turning out-of-plane is much greater resulting in a better overlap of the $\ce{C-H}$ bond with the ring system and thus a lower $\mathrm{p}K_\mathrm{a}$.