I used to shoot tennis back in the 80s, and was pushing my 400 to 800 or 1600 to get anything decent. Same for AFL (Australian football) - pushed the 400 TriX to 800 and 1600, and I was shooting with a 300 f2.8 lens.
The tennis was lit for the ATP Tour, so not the usual club stuff, and the AFL for pro football. The 3200 will be fine shot at box speed, if you choose to shoot 200, I'd push to 800 (I did actually push APX100 to 1600 - grainy as, but still gave usable images.
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That was an experiment for me - in case I *ever* got caught out, and surprisingly it showed me that I could most definitely get useable images if 100ASA was the *only* stuff on hand.
Give it a whirl - you never know what you can achieve, if you don't try.