Quick answer - Shantam to the contrary, yes. But let me explain.
Nick Alexeev provided a spectrum from a typical white LED. While it is not a faithful simulation of an incandescent (the big spike in blue is notable), it does contain all visible wavelengths. Your question asked "Does a light like this produce a full spectrum of light, such that appropriate light filters could produce any spectrum of visible light?", and the answer is obviously yes. If you wanted a predominately green light, for instance, it wouldn't (relatively) be very bright, but you could do it. This is not true for RGB LEDs, which would have very narrow spikes of intensity at 3 different wavelengths, with nothing in between. So, while you could easily produce a subjectively yellow light from an RGB LED source (just transmit red and green in the proper intensities), a narrow-band yellow filter would transmit nothing.