I would say yes, 6 or 7 days of electrolysis would do it good. Maybe 3 volts and 1/4 to 1/2 amp in a 5% sodium carbonate solution. Just enough amps to make it look like it is smoking is where I get the best results. The encrustation will fall of easily in the first day or two. The oxidation doesn't stop until you stop it, even on silver. If it is fragile now, that condition will continue to get worse until you get the chlorides out. I say save what you can, that stone is a lot more interesting and valuable mounted than it is loose. It will be interesting to see what it was mounted in and if it has any markings.
Very nice find by the way........
Jason