Is the hydrogen atom attached to the benzylic carbon in benzaldehyde acidic? If benzaldehyde loses hydrogen atom at the benzylic carbon, the negative charge will disperse into the benzene ring via resonance. So shouldn't the conjugate base formed be stable, implying that the hydrogen was 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 $\mathrm{p}K_\mathrm{a}$.