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No. You will be amaze at how well it remove the materials. We use the plane and belt sander to scribe many projects.
The task here is to remove a calculated amount each and every pass, roughness aside. Accurate amount is a very loose term here as long as you can take a different cut and not over the same planed path then it should accurate enough. Most plane will remover up to 1/16 materials at each pass. It can be set to 1/32 to not stress the tool or blades. Buy an extra set of blades if available and you will use the plane on other projects. It should do the entire side without issues. Personally, I would remove 3/16 near the back for less fighting with stove and everything else back there.
Cheap ply or imported plywood? Look at the top layer of veneer from the edge. It looks to be some type of Birch or Maple from Asia, more then likely made in Viet Nam or Indonesia. The last ply or veneer is literally paper thin and it often comes off by peeling with one's finger nail. Its inexpensive compared to a domestic (shop) Maple, at half the cost. We don't use it. Call back on a 30k kitchen cabinet job would be a nightmare due to de-lamination of a piece of plywood. No thanks.
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