I teach air accident investigation techniques and many of my students (about 50% do not have degrees) Most from the government agencies (ala AAIB/NTSB types do. The 50% that don't have engineering degrees often include pilots, and mechanicaly inclined looking to work within organizations in aerospace.
Here are some links to ask some questions before you embark on such a career.
http://www.scsi-inc.com/
http://isasi.org/
Good luck and say hello if you ever take one of my courses.