The short answer is yes, steroids can cause diabetes in some cats, and nearly certainly cause diabetic cat in remission to come out of remission (or a cat with "transient" diabetes to have full blown diabetes). The largest contributors are two of the most commonly used steroids, prednisolone and dexamethasone, but other orals can also cause blood glucose to raise. I had a night where Bandit's BG rose 100 points because he was grooming my other cat and ingested a very, very small amount of Orpheus's ear drops that contained a steroid that had gotten on the fur around his ears.
That said, there are some life threatening conditions that absolutely need to be treated with steroids because those conditions are more serious than the diabetes. Bandit was in that position back in March when he was diagnosed with myelofibrosis, and he needed to go on prednisolone and immunosuppresants or he would have died. Once he started on the steroids, his blood sugar shot right up into the 300s and he had to go on insulin, and his insulin need lowered as we slowly lowered the prednisolone dose. I think he was up to 1.5u of Lantus on his full dose (10mg), and went down to 1u on 5mg, and so on. He went back into remission about a week after we stopped the prednisolone completely.
I would second trying out the Flovent--I know there are members here that have used it with their diabetic cats with good results. As far as I know, it doesn't raise BG like the oral steroids will. Cyproheptadine (an antihistimine) and cyclosporine (an immunosuppressant) have also had success with asthma in some cats, so you might also want to see if one of those works before going to the oral prednisolone, which I would say should be your last resort if none of the others works because of your cat's diabetes. I do know that cyclosporine isn't really recommended for long term use, because it's an immunosuppressant.