Whether you need a tuner or not depends on what you're trying to do.
If you're looking to watch live video "as it happens" on the car, such that you could possibly drive the rc car from that view, then you will need a TV tuner such as the Avermedia AverTV PCMCIA Card or a USB solution. The PCMCIA card should offer the best recording quality and portability since it is powered off the laptop and will have plenty of available bandwidth. If the laptop is only USB1.0 then a USB tuner is out of the question due to the lack of bandwidth afforded by the USB1.0 specifications. Some external boxes will be specified as USB1.0 compatible, but in my experience none of them can provide a decent quality image at a good enough framerate. If the laptop is USB2.0, you will get better results but the box will probably need another seperate, external, power supply.
If you simply want to record races whilst you drive from the normal viewpoint (ie you do not need to watch the live image) then you can simply get a MiniDV camera with USB or 1394 (Firewire) linkup and copy that over to the laptop afterwards.
Presumably weight would be an issue with these cars, as such you'd probably be better to go for the mini-wireless camera idea and record that via a tuner card/box, rather than go for the digital camcorder/firewire idea