I might actually have to try a radish daiquiri sometime. I found a recipe for Radish Sorbet (from Iron Chef)!
2 cups sugar
1 cup water
1 bunch red or icicle radishes (scrub the radishes and discard the greens)
1/2 pint strawberries
1 small seedless watermelon
1/2 cup Pimm's Cup
Juice of 1 lemon
Pinch of salt
Make a thick simple syrup by combining sugar and water in a medium sauce pan. Bring to a boil, whisking occasionally. Once the sugar is melted, remove from heat and let cool. When simple syrup has cooled, pour into a blender and add all remaining ingredients and liquefy. Taste to make sure the radish flavor is there. If not, add more radishes. Freeze in an ice cream maker according to manufacturer's instructions. Number of servings = 8.