I'd wondered about that connection myself... My acute onset diabetic, Mr. Sluggo presented with vomiting anorexia and dehydration at the time his DM was diagnosed. I think in retrospect, it was "true, true, and unrelated". In his case, a series of prednisone injections probably exacerbated his smoldering glucose intolerance to frank diabetes, and likely gave him a bout of acute pancreatitis (never properly diagnosed with blood work, but suggested by the vet) as well. Vomiting is common with pancreatitis and with DKA. I suspect your kitty had one of those two superimposed. Mine had the former, but N/V can be prominent in DKA as well. Plain, simple diabetes... not so likely.
JMHO.