The issue with these sorts of light sources isn't the color temperature, but rather the spectrum provided by the light.

A camera (or your eyes) can only record colors which are reflected from the objects in the scene (not counting objects which have fluorescent properties). If the light shining on the object doesn't contain a certain color, it can't bounce to you, and therefore the color of the object can't be recorded in the way it might be under full spectrum light.

In your specific example of a sodium-vapor light, the color spectrum looks like this:

CC-BY-SA image from Wikimedia Commons, author Philips Lighting

You can see that there's a very narrow spike of light just short of 600nm, which is quite yellow. Everything you see (or photograph) will be in terms of how the object reflects light in that narrow band. So your assumption is correct — you can shift what is recorded as neutral grey/white, but your chart will probably look quite strange and "inaccurate". And there's really nothing you can do about it besides bringing in other lighting.

If your other lighting is also narrow-spectrum, that will improve rendition of the colors it adds — pretty simple, except when it comes to getting everything in your scene lit the way you'd like it to be with each different color. And your white balance will need to be more of a compromise (probably you'd pick something which would preserve both strong color casts, rather than attempting to neutralize them).



More details are covered in several existing questions:

Best fluorescent bulb color temperature for shooting people and interviews?

What white balance settings do I need to capture the cast of a coloured streetlight?

When should I use manual white balance settings?

How does the colour of ambient lighting affect colour rendition?
Here is a photo of a menu in Bali, Indonesia:



The Diet Coke is 14,000 rupiah. The regular Coca-Cola, and other soft drinks, are 10,000 rupiah. It isn't just this restaurant, the same is true of virtually every restaurant I have been to.

Why is Diet Coke more expensive than regular Coca-Cola in Bali (or Indonesia, if this is not limited to Bali)?
