Storm - I researched the aircraft capable of "super cruise" and did not see the T-50 listed as a super cruiser (like the F-22, Su-57, J-20 and maybe F-15), so the T-50 has to use burner also to exceed Mach 1. I also saw several articles that stated the T-50 was originally "designed" (or perhaps marketed) as Mach 1.5, but is now only going Mach 1.1. I have not conducted extensive research on the matter. My understanding is that the T-7 was designed to exceed Mach 1, but has still not been tested in the supersonic regime.The airspeed being lower is a limitation of the airframe, not the engine power. I am confident that if the pilot leaves the T-7 in burner, it will easily slip through Mach. It looks like the US Navy is vetting the T-50, the M-346, and T-7 as an Advanced Trainer for FCLP and Aggressor Roles al. Since the Navy is doing away with the T-45C and also CQ (Carrier Qualification) using Dedicated Trainer. It appears they are going to use the new jets for FCLP only and do the CQ in the Simulator and then live with an F/A-18F Super Hornet. The E-2D community will train FCLP and CQ in-house on that type. From the looks of it, LM is way ahead of their competitors on this contract as well as the next Advanced Trainer Program with the USAF. Looks like they will have that RTG before the T-7 enters service.
If you want to be 100% accurate, airspeed is based on flight testing (specifically flutter testing). At least as far as the public is concerned the T-7 is currently tested to Mach .975. The aircraft is computer designed, but extensive flight testing is still prudently required. It is possible the airframe could exceed expectations and be capable of handling a more powerful / faster engine. I guess turning on the burner is adding engine power...right?
With regard to Navy Fleet Carrier Landing Practice and Carrier Quals, the whole "new" thought about "no" Training Command (there is a difference between the Training Command and the Replacement Training Squadrons) Carrier Quals is based on flight control software in the F-35s and F-18s. It is still to be seen if the Navy brass will go for that. For example, the F-35 that kept flying after the pilot ejected a couple years ago shows pilot's are relying too much on the software and forgetting that the aircraft still flies without software. The pilot in that case failed to rely on his tertiary instruments, ejected and the plane continued to fly for 60 miles or so. The pilot is no longer a military pilot and the aircraft is no longer in service.