Use "noise gate" to paste room tone?

Paul-L’s De-Clicker plugin can reliably remove the brief (<5ms) high-frequency (>2kHz) lip-smacking clicks without damaging the clicks which are part of speech, see … Trying to meet ACX specifications - #19 by Trebor

Tackling other clicks is more difficult as, apart from context, they can be indistinguishable from legitimate speech clicks.