It probably can't support a K6-2+ or K6-III (as they have on chip cache), and they really benefit boards that can be jumpered for higher bus speeds anyway (75, 83, or 100 MHz).
They will typically boot fine albeit mis-identified and there exist utilities to configure them correctly after boot-up, but the real issue is the voltage regulators. Those chips would stress the 12A regulators of the venerable TX97-XE socket7 board to the max, esp. the 2.4 volt versions.
I would highly doubt this particular SBC could reliably sustain this kind of load, it just doesn't seem to have been made with those chips in mind.
But if it could, then it's the on-chip full speed L2 cache of the K6-III that actually makes it perfectly suitable for lower bus speeds - the higher the discrepancy between CPU and system bus speed the more profound an effect the local cache has.
On my rev 4.1 GA-5AX with a 2.4V K6-III @ 400, I actually preferred the 66 Mhz setting because it enabled the motherboard's tag-RAM to function properly (not so at 100 MHz), thus letting the motherboard's cache function as L3 cache with the K6-IIII.
Overall performance was perceptibly snappier and only tasks involving huge RAM I/O loads would be somewhat slower.