I have done the same itinerary (arrive on BA from LHR in C with hand baggage only) several times, know my way around FRA very well, and would strongly recommend to NOT choose that train. While theoretically possibly to catch the train in 30min, my experience has been 40-70min:
- 2/3 times I arrived at a bus gate and it took 20-30min to get dropped off at T2
- only 2 immigration officers for another flight and mine
- 5min wait for the Skytrain
plus some time walking (>10min)