Or does the color checker have another option for white balance.
There are different version of the X-Rite ColorChecker, or from other brands. Usually they have some neutral gray patches which can be used for post-production white balance.
Other products may be used for in-camera white balance before shooting - using a "white" (usually a very light grey) larger patch.
Some products like X-RIte Passport include different types of patches, including the white balance ones. There are other products with only white/grey surfaces for white balance only.
Products like the ColorChecker beside white balance comes with software (or can be used with) that lets create a specific camera profile for a given illumination taking into account not only the spectrum reflected by a "white" patch but the behaviour with a number of different target colours - to try to deliver a more precise colours output. This requires anyway a fully calibrated workflow to be really effective.
For B/W documents, and anyway where colour match isn't critical, a simple white balance is enough, otherwise creating a specific profile may save a lot of post-production time.