There were a few programs for displaying copper coloured pics on the workbench on AmiNet years ago (can't remember their names though) but they were very tricky to edit/create pics with and the results were pretty poor, think thats why they didn't catch on... 
Well, the resolution would be pretty crap, but on the other hand, you'd have 12-bit true color. Pictures shouldn't be that hard to generate, so I'd blame it more on poor tools than any actual complexity of the task (really, all you'd be doing is a straight chain of MOVEs with WAITs at the end of each line.) Probably work better with visually simple, color-heavy images - the Windows XP "Bliss" wallpaper, for example, would look pretty good.
I was wondering if one could use a single bit plane for higher resolution and switch out the single color register with a new color. I am not for sure how it would be timed or even be fast enough.
That was basically what I was thinking of doing, but it's fairly slow - you could only achieve 80x(height), and even that might not be reliable.
You're pretty much right, as far as I remember. The caveat is that anything else that can steal DMA cycles will cause the copper to miss one or more colour changes, and the blitter and CPU will pretty much stall on any accesses to chip RAM while you're doing this. In other words, any disk, audio, display or sprite DMA can or will interfere.
Bummer. Probably not very stable, then - 40-wide might be a better shot, but then you're getting into ridiculously low resolution...