Yes, it will work fine to put a cheaper type of lumber under the top plywood layer.
If you want two layers of plywood, one way to save a little money is to cut a 4x8 sheet in two -- but not in half. Most people will find 24" to shallow for a work bench. So cut it at 26/22 or 28/20 and then position it so the double thickness is where you do most of your work, with a single thickness in the very front and/or in the very back. You'll get most of the sturdiness of a 1-1/2" thick top without having to spring for two sheets of stock.
I don't have a great picture of it, but if you look at the bench folded up against the wall, you can see that I have 2x 3/4" sheet for the rear 20" and then a 2x4 crossmember capping where the 20" deep support sheet stops. It might not look like it, but this is a very sturdy work surface.
But if it's a fixed bench, you can also put a few inches of space in the back, too. Again, the point is that you need the reinforcement (usually) right in the middle of the work surface.