You could do it that way though it may bulk it up, but you are looking to do a wide ledge so it would be fine, or you could attach just the 1x and skin it that way, save a step and some money.
Either way as long as you attach any lumber that stitches together the 2x members you will gain shear strength/no racking.
I would probably do a ply top and bottom and face w/ the 1x for what you are going for.
The pre finished 1x is a little more expensive than the plywood, but it's already finished/stained so saves a step there as well as finish material cost.
You could glue and clamp boards on if you do it properly, but it would be nice quicker and easier if you had a pin nailer to attach those boards.