Yes, I have used Airbus FMGS and FMGEC (IRS and GPS referenced), on an almost daily basis for many years' airline flying.
Yes, But, I'm sure you haven't done so by wafting from side to side chasing the magenta line. Rolling from side to side you will have a lot of sick passengers. In the cruise at 400 KTS drift is minor consideration but on approach at 140 -160 kts it is not minor. Pitching and rolling whilst chasing the indicated parameters is not the way to do it. Heading and time remains the way for a smooth ride.