Can someone help me understand the advantage of Killdry?  I have one H9 that I use in my amplifier's tube drive, buffered FX loop.  If I use Killdry what (if anything) will it do with my tone?

The purpose of KillDry is to (wait for it) kill the dry signal, so the MIX control just adjusts the wet level. It would normally be used with a parallel effects loop or in a mixer effects send/return setup to avoid having adding the dry signal from the pedal to the effects loop/mixer dry signal.

Beyond this, it should not affect the tone.