Zapata,
Yes, my travel anywhere, carry anywhere, shoot anything anywhere double is built on a shotgun action.
It was custom built for a mate of mine by a smith who had built at least 6 other similar doubles.
To cut a long story short, the smith f*cked the regulation up and it shot 12 inches apart at 50.
I bought the rifle for a song and sent it off to a smith who had regulated a lot of doubles.
He reregulated it.
The gun now shot into 1 inch at 50.
Trouble is after 30 shots his solder let go at the wedge.

I said "to hell with gunsmiths", and stripped and rebuilt the barrels totally myself and also did the regulation myself.
At the same time I fitted a scope using a base I designed and machined myself.
That was more than 3 years ago.
The gun now shoots 4 shot ragged holes (2 from each barrel) at 50 yards.
It is a great rifle and I've shot a lot of game with it.

A double rifle can be built on a shotgun action but there are many things that can affect how well it will turn out.