Touch-up machining is sometimes done after anodizing, painting & plating. Very limited, usually, for threads, o-ring areas, electrical contact areas. It's often difficult for a masker to manually apply tape or liquid (with a fine, artists paintbrush) to the precision on the blueprint.
I would recommend machining first. Only do touch-up machining to remove overspray, provide sharp coating lines and expose electrical contact areas. Maybe can save $ not skipping the masking of difficult-to-mask areas.
Also, first take a painted part to your machinists, show them the rough paint edges, and ask how they would do it better & w/o hurting the paint. They can if they want to, so make it their decision as much as possible.