I have some rough cut wood, I don't have a plane, I want to turn them into some crates for storing beer.
Could I just paint them?
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Painting rough cut lumber will only smooth out the irregularities a very marginal amount. It will take many coats to smooth it out any significant amount. Plus, depending on how rough your rough cut lumber is, you may have trouble with adhesion.
I'd at least hit your wood with a 60 or 80 grit sandpaper to remove the roughest parts.