I think it will dictate the rear roll center which will affect how the car behaves on some level, but yes, it should not affect roll rate.

I am considering a Watts on my car, it will allow me to run more tire without rubbing the fender.

As for bigger than a '73 bar, you can step up to running a tubular 1.5" bar with adjustable arms, that will require some fabrication to mount up. If you do a 2" tube with bushings to mount it, then want to go to a larger or smaller bar later you can use the same mount, just change the ID of the bushings to match. Not sure what bar that would dictate on the rear. I imagine to get what I want I will probably have to make it anyway. I will start out with a 1-1/8" '73 style bar on my car on the front and no bar on the rear and see how it does, then go from there.