@JemimaPyjamas I'm afraid I don't know enough to answer that. What kills is inflammation due to the disordered immune response, sepsis, and lack of oxygen to the organs.
I've just had a quick look at the literature around sepsis, but it's confused. Diabetics are more likely to get sepsis, but that's usually more due to the increased prevalence of skin sores. There are few papers looking at outcomes of sepsis in diabetics, and even fewer that distinguish between insulin-controlled/not or by Type, and also few that account for confounding factors (things that confuse the picture, like people with Type II tending to have other problems like heart disease, which makes outcomes poorer).
This paper ccforum.biomedcentral.com/articles/10.1186/cc7707
says kidney failure is more likely in sepsis with diabetes, but (good news here) lung failure is lower, and the lung failure is more likely to kill.
The same paper, a large survey of effects of diabetes in critical care, referencing a number of other studies, concludes that the picture is very complex.
Please speak to your diabetes care team if worried, although it looks like even the consultant might not be able to answer your question.