That is, as long as shutter speed > frame rate. You can snap a 1/4000th exposure every 1/24 of a second. But if you need to snap a 1 second exposure, you can't achieve it unless you've got multiple CCDs or shutters, in fact, you'd need 24 CCDs/shutters, each "opening" to take their image 1/24 a second later.
The result on most video cameras of using "candle mode" is a severely jerky image that looks like you're on LSD.
On the other side, if you are snapping 1/4000th exposures, you end up with the "sports video" look (or "Gladiator" fight sequence stuff) You get images with no motion blur, but they are less pleasing to the eye.
Frame rate is fixed. If you need alot higher exposure than the frame rate, and artistically, you can't use a larger aperature, then you'll have to go with faster film. But faster film has annoying grain, so you'd need to clean that up in post processing, unless you want that effect ("Collateral")