The paint almost has to slow the etching process compared to the naked copper around it. The only way this wouldn't be true is if it quickly dissolves or reacts away when exposed to the etching solution. You could answer that - and your overall question - with a quick test. I predict it will be fine.
Be sure to specify which etching chemistry you plan to use - it might matter.
I have made many low-resolution PC boards by painting the pattern with fingernail varnish, using both Ferric Chloride and the Nitric Acid/Hydrogen Peroxide solutions.