The MMR vaccine contains three live (weakened) viruses, so there is a chance of very mild symptoms. The advice given to parents is to give calpol (paracetamol) if necessary. My son had the mumps, rubella and measles vaccines separately because it was at the height of the controversy over MMR and autism. He developed type 1 3 weeks after his 2nd measles vaccination, which I believe was the final trigger (any virus would have done it, just a matter of time), so I can't tell you how it affected his levels!
But do get yourself vaccinated, as it's a nasty illness and would really affect your diabetes control if you caught it. My Grandma had measles as a child and her ear-drums were irreparably damaged, leading to permanent deafness.