Iodine gets reabsorbed in the solution because of the following reaction :


turns the solution orange.
About the reaction with KOH, I think it is possible (of course, there will be competition between that reaction and the one above that produces KI
3), although I vaguely remember reading somewhere that a hot concentrated solution can result in the formation of

. In that case, everything else in the reaction remains the same, just replace KOI with KIO
3I think you're idea of a disproportionation reaction is correct