Tgrisham, that's an interesting question, to which I can't give a definitive answer, but I can offer some thoughts.
To the extent that high damping factors may be advantageous with a particular speaker in a bi-amped configuration, I would expect that the high damping factor would also be advantageous in a bi-wired configuration, but to a somewhat lesser degree.
However, my feeling is that the extremely high damping factors that Class D amps commonly offer are overkill, and the sonic differences those amps may have relative to other amps are most likely due to other factors. And with some speakers, a high damping factor will actually be disadvantageous.
First, consider that damping factor = amplifier output impedance divided into 8 ohms. A ten foot run of very heavy 10 gauge speaker wire has a resistance of approximately 0.02 ohms for the 20 foot round-trip that the signal has to make. That means that even if the amplifier has an infinite damping factor, the damping factor seen by the speaker would be limited to 8/0.02 = 400. And that neglects the resistance of the connectors and the wiring inside the speakers, as well as the possibility that the speaker cables may be narrower in gauge or longer.
Damping factor can be important for two reasons, as I see it: Damping of back-emf from the speaker drivers, particularly the woofer, and interaction of amplifier output impedance with the speaker's variations of impedance with frequency.
In both a bi-amped configuration and a bi-wired configuration, back-emf energy from the woofer will be conducted directly back to the amplifier, where it can be effectively damped by the amplifier, assuming the amplifier has a reasonably good damping factor. In a single-amp'd, single-wired configuration, a small but conceivably significant fraction of the back-emf may be conducted across the jumper, or through the speaker's internal wiring if the speaker has only a single pair of terminals, to the mid/hi drivers, where that fraction of it will not be effectively damped and where some of it (at frequencies that are in the crossover region) may be re-radiated as sound. That may or may not be subjectively preferable.
To the extent that the amp does not provide complete damping of back-emf in the bi-wired configuration, some small fraction of the back-emf energy may also reach the mid/hi drivers, through the wiring from the amp to those drivers, which is why I indicated that bi-amping might provide marginally greater benefit in terms of damping.
The second factor I mentioned, effects on overall frequency response resulting from interaction of the speaker's impedance vs. frequency characteristics with the amp's output impedance, I would not expect to differ significantly between a single-wired configuration, a bi-wired configuration, and a bi-amped configuration (assuming identical amps). The most significant factor in that regard would be whether the particular speaker design was voiced based on the expectation that it would be used with a very low output impedance/high damping factor amp, such as most solid state amps, or with a high output impedance/low damping factor amp, such as some tube amps, or with some compromise in between.
Note that Atmasphere's very highly regarded OTL tube amps have damping factors on the order of 2! Which means that they will tend to deliver a power level into the speakers which is relatively constant as a function of the speaker's impedance vs. frequency variations. While a more conventional low output impedance/high damping factor amplifier will deliver an output which is constant in voltage relative to those impedance variations, while delivering increased amounts of power at frequencies for which the speaker impedance is lower. See Ralph's paper on this subject here:http://www.atma-sphere.com/papers/paradigm_paper2.html
The common sense bottom line, imho: Amplifier/speaker synergy is critical; damping factors above a couple of hundred or so (and possibly well under that) are useless and are not the reason for the sonic signatures that Class D amps may have; and bi-wiring is largely a matter of trial and error and user preference.