My 35L focuses as fast as my 85 f/1.8 in the same lighting conditions. With reasonable contrast subjects, focus is almost instantaneous with no hunting in room light that requires an exposure of 1/40, f/1.4 ISO800 using my 20D.
I've used the 85 f/1.8 for shooting a few volleyball games in our church gym. I've not used my 35L for VB or BB but I'm confident that the 35L would perform well, as far as focus speed and exposure, under the hoop in basketball. BUT, it may not be wide enough unless you can get back 3 or 4 meters. If you have access to the gym and a zoom that covers the 35mm range and wider, stage and check a few shots under the hoop to see what FL is appropriate.
DOF at ~2M, f/1.8, is sufficient to capture most of the body thickness in acceptably sharp focus.
Even if you only occasionally use the 35L for under the hoop shots, it will pay for itself in the pleasure it gives for everyday usage with the beautiful colour, contrast and bokeh - not to mention the crisp images it gives.
A f/2.8 zoom is far too slow to stop action of a volleyball and I expect the same for a basketball.