Hi Nat, it more than likely depends on the equipment it's feeding. For instance this dCS kit requires a 44.1KHz word clock & it converts from that for DSD which is 64 times the frequency.

I have seen studio type DACs that need different word clock frequencies when using different sampling frequencies. When i was looking into the word clocks i couldn't help but notice If you take a look at something like the Apogee Big Ben i think you'll see what i mean There were others i found & every one could output multiple frequencies (though obviously not at the same time)

I have a feeling that if your clock only happens to output one frequency you might have to upgrade, though don't take this as gospel, it'll depend on the DAC as well