Does Kohlrabi grow its bulb under the soil? If it does then you will most likely have rotting problems. I have no experience with Kohlrabi, but if it does grow the bulb above the soil/water line, then you should have absolutely no problem. As bushwackxj mentioned, the leaves will do very well in the DWC.
You said that your pH was 6-7.5. This is a bit too basic, you should try and aim for a pH of about 5.5-6.5 with most hydroponic crops.
When I grew lettuce in the DWC, it absolutely thrived! It was too successful, and actually weighed too much and made the netcup fall into the hole in addition to overcrowding my basil. I'm expecting really good results from you!