If you get one that's designed for archtops and attatches only at the side, that probably will affect tone, but if you're willing to have holes dirlled in the front they do make a model for carved top guitars that screws on. Which is closer to a stop bar, so I'd imagine doesn't sound a million miles away from one.
I know if I ever get a LP it's getting a Bigsby, and that's all there is to it. They look awesome. I know Jimmy Page had a LP Custom with one, sadly that got nicked, but I reckon that was one cool guitar, no mistake.