To the Bahamas in calm conditions (a daysail basically), but not much further than that.
They lack righting moment, that's the problem. Not quite self-righting from a broach.
Presto was a modified 'round bilge' sharpie:
"I was lead to make a try for still greater stability...adding a little deadrise, and increasing the depth of hull and bilges to give ample displacement and righting moment. Thus, with slightly rounded bilges, and clean entrance and clearance we arrived at 'Presto'."
"...she never heeled enough to take water over the cockpit rail in the six years that I sailed her from Cape Cod to the Gulf of Mexico, in all kinds of sea and weather. ...She was one of the most wholesome and satisfactory boats I ever owned."
--excerpted from "The 'Presto' Type of Centerboarder",
In addition to being built light and very strong, Reuel Parker's boat has an arc bottom, and the bow stays in the water, as seen here
. Since the original Presto traveled between New York and Biscayne Bay on her own bottom, assuming competent handling by the crew, you should have no problems going anywhere you want in this boat.