The body clearly can convert Iodide to Iodine since Iodide acts as an antioxidant which results in it's oxidation to iodine. There may be some benefit to taking some as free Iodide rather than Potassium Iodide also.
Dr Brownstein says in his book that he used various iodide preparations with mixed results but he didn't say what they were nor did he say at what dosages. so more KI may have given better results.
I used reduced Lugols because it's much cheaper in the uk even more so than KI, but now since I managed to find a even cheaper source of Ph Eur grade KI I'm using that which I think is preferable in gram doses.
Definately though, where a particular disease responds to Iodine then I'd use the necessary amount of that, but my problems including ulcerative colitis all seemed to respond well to the iodide and best around a gram a day.