No, in the interest of safety, the engine keeps running and the car can still be driven when the key goes out of range. This is a necessary safety precaution, so you're not stranded or the engine dies suddenly if the key's battery goes flat while you are driving. So, the key gives you keyless access and engine starting, but is not needed for continued operation. However, once the engine is shut off, it cannot be restarted without the functioning key in range.