As I said for anything indoors, anything at night or even heavy overcast, if you want to stop action you really should have a 2.8 lens if shooting with a 6D...this is both for being able to have high enough shutter speed to stop action as well as to have autofocus (with center point alone on AV mode). With my 6D and the 70-200 2.8 I can get pictures in these situations. With my 100-400 I simply can not even at iso's >12000 which aren't ideal. To be honest even with a 2.8 lens sometimes it's not possible at night games. Kids fields aren't always that well lit.
That being said I can get great pictures with a 2ti and the 100-400 in the middle of the day