Sure, if you plan to paint the cabinet interiors, you can lightly scuff the surface to help the paint adhere better. I recommend using 220-grit sandpaper. An orbital sander is my preferred method, but smaller areas can be done with a sanding block and 220-grit paper.
After sanding, apply at least one coat of primer followed by two coats of paint. This should create a durable, long-lasting finish that can also be touched up or repaired easily in the future.
You can also leave the cabinet interiors as they are, with the clear-coated birch plywood finish. This is the most durable option, and the natural birch grain does a good job of hiding dust, dirt, and minor imperfections.