Flopper stopper question.

Retractable foils instead of flopper stoppers

Could we use retractable foils on both sides of the boat instead of flopper stoppers?

 

Yes, but they don't work in a very intuitive manner. They resist roll as a function of angle of attack, and need operate at a small range of speed and roll rate to be effective and justify their drag and not stall. Better to keep them in the water like a keel.

Your picture seems to imply that there is some angle of attack that would be producing lift at a steady condition. This is in fact bad and is not stable, or at least it does not improve stability. What you want is an angle of attack that is a function of roll rate, not roll position. Velocity and position are 90 degrees out of phase. A fixed AOA relative to the surface would only add to drag and not produce more damping than a fixed 0 degree foil.

 

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Your illustration is similar to DSS foils that work very well on sailboats by increasing righting moment and lifting the whole boat. They also improve the ride considerably according to the designer and owners of DSS boats.
You might find this interesting: http://www.boatdesign.net/forums/sailboats/quant-28-foil-assist-keelboat-dss-38421.html