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Probably yes except for any convex curves you may have inside, although you'll have to be careful not to pull the lamination's apart
Depending on how much you have to do and how perfect you want it, I'd be tempted to make a template out of a thinner material and working off that. If you have a router you can get a flush trim bearing bit to then transfer it to your final piece.
If it's getting painted then you can always fill any gaps with caulk afterwards.
Here's one I did a few months ago.
https://www.lfgss.com/comments/14455103/
Hovis
TvH
Birch ply. Easy enough to get a curve on something with a traditional block plane?