Most likely not - they will be operating under Par

Most likely not - they will be operating under Part 91 which makes flight plans optional. I cannot speak for whether or not Kalitta's company policies require flight plans to be filed. I have seen many operations that require flight plans but allow them to be filed as local "strips" with the control tower as test flight areas are generally close to the home airfield. In that case, we won't be able to know if 706 flies (save for orvie's word). If they are required to climb over 18,000 feet for pressurization checks they will be required to file a flight plan, but I cannot say with certainty that they will need to do that.