There are a number of airfoil families where the designers of the family basically just increased the thickness ratio. The increase in thickness often gave a greater AOA with an associated increase in max lift before the stall.

Of the few I've looked at, the L/D was pretty much the same. So the induced drag differences won't probably matter. However, parasitic drag is what it is, so if you keep the same chord, you will see that increase. Will it matter? It did in C/L combat airplanes that flew in the 120mph range.

Do you have some airfoil in mind? Symmetrical? Undercambered? How fast will the design be expected to fly?