As long as the paint you are using doesn't get on the surface of the ball you should be ok. Engraving typically sits slightly below the surface so it should be ok.
Technically the USBC has a rule that no foreign material can be on the surface (paint, sharpie, etc.) But repainting the engraving should be fine.
There used to be a company that sold a kit to recolor bowling ball engraving, but I forget the name of it.
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