Does the quality of life drop if you have type 1 diabetes?

Depends . If you define higher quality of life as crusing thru it with minimal worry about your health & few contacts with doctors, i guess you can say it does. Of course that philosophy may tempt you to adopt bad habits that will do more harm than t1dm & lead to premature death. Well controlled dm patients often lead very enriching lives with an appreciation for the health they strive to maintain.
Not necessarily. If well controlled, can have excellent quality of life think of sport figures, actors/ actresses, marathon runners with it mary tyler moore, etc.