The chances are better now thanks to courses like DAFNE, increased use of pumps and generally more of a 'can do' attitude. When I was a teenager in the 70s/80s, the rule was if it involved shift work you couldn't do it. No discussion, no asking what career you wanted and finding a way, just "you can't". With modern insulins and flexible MDI, its quite normal for type 1s to become nurses or doctors now, or for those diagnosed as adults already in the profession to continue their role. Hopefully therefore the proportion will increase over time.
My hospital has had diabetic DSNs for at least 10 years. Currently at least two DSNs are type 1, one on DAFNE and the other on a pump. They are of course the best and most respected due to their knowledge from both sides of the equation.