There's really no difference between paint and varnish except for trhe opaque pigment incorporated in the paint. I think that some of the "sunburst" finishes popular on archtop guitars could qualify as painted.

The only problem (aside from looks)in panting a guitar is the additional mass of the additional finish which will tend to deaden the sound. You could get the same deleterious effect from adding more varnish--you'd just have to add a bit more to make up the added mass of the pigment.