Ken, do you mean recording the webcam's stream to a laptop hard drive? If that's what you mean, there are plenty of webcam utilities that will do this. I use WebcamMax:
http://www.webcammax.com/ which also creates multiple Webcam's from a single stream so I can use it in multiple applications.
You might be able to use your digital camcorder as a webcam via the USB or Firewire port. That is going to vary from model to model. If not, then you can get a USB Video capture device that will create a Webcam out of the Camcorder's RCA composite video out (the yellow plug). Check out
EasyCap Make sure you get one that's compatible with your version of Windows. Scott Bennett, Steve Miller-OK, or the ChaserTV guys are good ones to ask as they helped me setup my Webcam hardware.
I'm not sure about memory consumption, but I don't think the entire stream is loaded into memory, only small blocks that are temporarily kept. I think hard drive space is the bigger issue, and as long as you have a modern processor (a Core 2 Duo would be ideal), I think you'll have no problem multitasking with this running in the background.
Are you just trying to record your entire chase? I thought about using a webcam to do this, but I finally settled on getting a harddrive camcorder. My Sony HDR-XR500v records something like 18 hours in high definition. With a harddrive camcorder, you don't have to worry about the state of your laptop or running additional software. If your laptop shuts down in the middle of recording your webcam's stream, you'll probably lose the entire stream.