No, you can't get diabetes from blood transfusions. Even if the donor was a diabetic whose blood was full of glucose, a normal person should be able to process it quickly, no problem. Type 2 diabetes is a condition where the cells in your body become resistent to insulin over time and/or a person's pancreas stops producing enough insulin (often because of long-term high blood sugar). It's not something you can catch from blood contact, otherwise that would be well-known.
I think it's more likely that being ill lead to him being more aware of his diabetes or made him actually go to the doctor to be tested.
Again, I think it is very important for your husband to go see an actual Endocrinologist instead of relying on the advice of a nurse who is not specially trained for this type of thing. Controlling his weight and getting more exercise is important, but that is a long-term plan. In the short term, he has really high blood sugar that is putting him at real risk for kidney damage, extremity tissue damage, and stroke. He needs short-term treatment to get that under control. Perhaps, over time, he can get his weight to the point where he won't need medication anymore, but that could take months or a year or more. Having untreated diabetes for that long could be very dangerous. Please go find an actual trained Endocrinologist and get his or her advice on this.