When cutting the Turkish delight, it will likely help if you make use of confectioner's sugar (often already present in packages with Turkish delight) - otherwise, the pieces are very likely to stick together. For the same reason, add the pieces to the (almost) finished ice cream, and not to the ice cream machine during churning.
While the amount of sugar might seem low, this is made up for with the inclusion of the Turkish deligths (which, to a large extent, consist of sugar).