It depends on the kick drum and the rest of the kit. If the kit is loose and resonant (I call that sloppy...) then yes I'll use gates to create a new envelope.
Sorry, not to stir things up here, but please explain to me what you mean by the bolded bit?
I've never ever considered harmonics when selection compression. I might use some sort of HPF/LPF/BPF for manipulating the detector, but it seems strange to me to consider harmonics when applying compression.
I gate. Less rumble/mud/junk even if not that audible in the mix it just makes me feel better and is a hell of a lot easier to compress and eq with more freedom.
Or I could give you some kind of BS answer like "I never process anything on drums. No eq, no compression, no gates, hell no fader even!" But then again I guess jazz exists! ha!