It's simple to correct if your shooting RAW because the WB selection can be made in post processsing. It's more difficult in JPEG, because the WB is "burned in" by the camera. However, if the colors are off in the JPEG image, you should be able to adjust colors in post to make it better if not exactly natural.
This isn't entirely accurate. As I have mentioned, WB correction is always done post exposure, either in camera or in the raw processor. The sensor chip really has nothing to do with WB, and this has been something that I've always been pretty disappointed by with digital - I always wished that WB could be set via gain, rather than via postprocessing. In fact, the spectral sensitivity of most DSLRs is this odd emerald-green color, the raw processor actually pushes the red and blue channels to a significant degree to compensate for daylight WB - all behind your back!
JPEG has no disadvantage in terms of color correction, what it is lacking is bit depth. All images, regardless of how the data is written to the card start out the same raw data off the sensor. When you choose jpeg over raw, the camera pushes the 10-14-bit/ch RGBG data to compensate for the selected white balance, and writes it to an 8-bit/ch RGB file. Now, if you've missed the WB on that 8-bit image, you've already lost the rest of the data, including that extra green channel which is used to compute luminance while being unaffected by the green/magenta correction (i think). This makes the correction much more difficult do accomplish without introducing banding or emphasizing noise, as now you have a palet of only 256 shades per channel, rather than the 2^10 to 2^14 shades that you do with raw.
But the same exact capabilities do exist to correct WB in raw as you do in jpeg, it's only that the amount of data you have available to do it is less on the jpeg, and also the jpeg has already been manipulated significantly by the camera to make that adjustment, in a sense, 'burned in'. But the adjustment is no harder in JPEG or raw, only with less data to work with.
