1999 Pontiac Montana

My 99 Montana with 160000 miles shifts hard at times and lost over-drive. I know it's time for tranny work but could it cause the ABS, TCS, and brake warning lights to stay on? It happened while playing in a snow covered parking lot! Checked all fuses, fluid, and new pads, rotors on the front. We have had the vehicle scanned at a local Advance auto parts store with only EVAP codes displaying. Also have taken it to Aamco transmission shop where we were told to overhaul the tranny and that there could be a problem in the braking system due to the lights - ya think? Anyway looking for not for profit advice! Thanks!