ever veneer over plywood to "save" a project?

Hi,
I'm using cherry plywood for the bulk of the casework on my current project, and have a fear that I may have already "over-sanded" in trying to even out the face frame with the sides (still have the final sanding to go, right before finishing). The side of the case is about 20" by 36", and I'm considering options to address any "self-inflicted wounds" that show up as I get closer to finish time.
Has anyone ever saved what might have been a lost project by re- surfacing a plywood side with a thin veneer? The surface is still nice and flat, and I would think that plywood would make a good substrate for a self-adhesive veneer. Also, the cost does not seem to be too prohibitive ($30-$40), when I consider the man-hours devoted so far to the project.
Is there some flaw in my logic? Other choices appear to be paint or firewood, and neither or those options sound very appealing...
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I'm sure it's been done and should work fine. However, getting a match between ply surface of cherry and a veneer might be tough. Ply always has it's own look to it in my experience.
Depeding on the configuration you could possibly also overlay with a piece of 1/8" or 1/4" ply and just trim out the edge somehow. Just not sure where this resides.
If you were sanding a face frame to get it flush with a piece of ply, one trick is to actually scrape the stick portion, favoring just a degree away from the ply and just pull the edge down until you just start touching the ply. I've done this on too many shelves to mention. My prefered is to leave the FF 1/8" proud.

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