Could airliners' wings be thinner if no fuel were stored in them?
No.

The wing thickness is primarily dictated by structural demands. It has to provide an aerodynamic fairing for the wing spar. Making it thinner would drive up the mass of the structure inside.

To simplify things, imagine the wing spar as an I-beam. It has two flanges which carry tension and compression loads, and a web between the flanges to transmit shear loads. The bending moment carried by the spar is the product of the forces in the flanges and the distance between them. If you reduce the distance, the forces need to increase to keep the bending moment constant. Bigger forces will result in bigger flanges to keep the stresses in the material below the yield stress.

Limiting the thickness is the desire to fly at a certain Mach number. A moving wing needs to push the air ahead of it aside, and thicker wings need to do more pushing. This results in a higher acceleration of the flow around the wing, and thicker wings have a lower critical Mach number (the flight Mach number when local flow reaches Mach 1). This drag penalty is especially severe in supersonic flight.

Thicker wings also help with creating higher maximum lift coefficients, up to a point. The plot below (taken from this website) shows that an airfoil thickness of 12% gives the best results, which helps to keep the wing area low. A thicker wing also makes it easier to integrate complex high-lift devices, which again helps to reduce wing area. 



The resulting wing thickness is always a compromise, and the fuel volume is only the result of that compromise. If a wing needs to store more fuel, the designers will choose a lower aspect ratio, but will leave the relative thickness unchanged. If less fuel is required, the tanks will become smaller, and again the thickness will not change.