Be careful when you add the "lip" (selfedge) not to make it so low that you can't open drawers. Also be aware of potential designs where you may be able to reach the drawer top to pull it out, then as you pull the drawer open your fingers get smashed between the drawer (with lots of momentum) and the lip (which won't go anywhere either!) This is a very painful experience. Keep especially in mind for fingers smaller than yours (ie kids and women) It may be that you end up doing a double layer of plywood on your counter anyway, and this isn't a bad thing. It allows you to lock in the top by overlaping your plywood seams, lifts the surface another layer's worth, and gives you more to attach your self edge to. Especially with tile, I would go for the extra rigid top.
Be sure to seal your grout after you install the tile. Grout is NOT waterproof. Which reminds me, us exterior grade plywood (CDX) for the underlayment, to help avoid swelling issues should it get wet.