I had the opposite experience. I was undiagnosed hypothyroid (Hashi's) for about 5 years. When I was finally diagnosed, my A1C was 5.7, but with treatment (first Levoxyl, now Synthroid), my A1C dropped (and has remained steady) at 5.2. I was eating very low carb the entire time.
I think it's the flawed thyroid rather than the Rx that can cause high BG. The same happened with my LDL. Undiagnosed, it was elevated, but it slowly came down to a normal level with treatment (Rx).