I was told if a patient is dyspnoeic on the ground they are going to be a damn sight worse at altitude
That's most certainly correct when talking about flying in airliners, most of which ( not the new B787, of course ! ) cruise with a Cabin Altitude of about 8000 ft. Anyone who is severely dyspnoeic on the ground is likely to be very distressed, and maybe even hypoxic and cyanosed, at that level.
However, the original enquiry was about a LAPL student, presumably in a light single like a C152 or a PA38, and who would seldom, if ever, be above about 3000 ft. Anyone with normal breathing on the ground should cope with that sort of level change with no problems.
