Absolutely. Depending on the model and accessories such as battery pack grips, etc., they can both shoot high-speed continuous sequences from 4 to 10 frames per second until you run out of film. The limiting factor is going to be available light. In order to shoot at the highest continuous speed, you need a fast shutter speed. If you are using a flash, of course you will be limited to the speed the flash can recycle.
With the digital cameras, there will be a limit as to how many continuous frames you can shoot in one burst. My EOS 10D will shoot at 3fps for a burst of 9 frames before it has to stop to write that data to the Compact Flash Card (it just runs out of buffer space). You can improve the time it takes to write the data to the CF Card by using the high-speed (40x) Compact Flash cards. I can't remember a time when that would have been insufficient, even shooting motorcycle road-racing. Even if I was shooting a crash-in-progress, it usually takes less than 3 seconds for the crash to happen. The delay while the camera writes the data to the card (using a 40x 512mb card) is typically around 2 to 3 seconds, then you are ready to shoot again. The last race I shot was before I got the 10D and I was using my EOS 3, but this next season I'll take the 10D with me and give it a try. I don't foresee any issues, though. The problem with the film camera is that they just won't stop the action for you while you load more film. With the digital camera, that's not an issue. I can get over 150 images on a 512mb card in RAW mode, and it only takes about 5 seconds to change the card as opposed to 15 or 20 seconds to load a new 36-exposure roll of film.