Can stress-induced cortisol reduce diabetes type I?
Short answer
Stress is not a good candidate to treat autoimmune disease like diabetes type I.

Background
Stress indeed weakens the immune system, and diabetes type I is indeed caused by an auto-immune response against the insulin-producing beta cells in the islets of Langerhans. However, autoimmune diseases like diabetes type I need chronic treatment (i.e., insulin treatment and dietary changes).

Even if stress would help reduce diabetes type I (admittedly, theoretically it could), chronic stress would also reduce the immune response against viral and bacterial infections, it would reduce wound healing and perhaps even increase the risk of contracting cancer (Glaser &amp; Kiecolt-Glaser (2005), as well as increase the risk of depression and cardiovascular disease (Cohen et al., 2007). 

Hence, it is safe to say that deploying chronic stress as a treatment against auto-immune disease effectively means substituting one life-threatening condition with another.      

References
- Cohen et al., JAMA (2007); 298(14): 1685-7
- Glaser &amp; Kiecolt-Glaser, Nature Rev Immunol (2005); 5: 243-51