I have seen weirder things; so I'd say it is possible.
Ah, clickogenesis. It seems to me as if such a process hasn't been observed yet. There are not many languages that have acquired clicks during their reconstructible prehistory: Dahalo (a Cushitic language), and some Bantu languages (such as Xhosa and Zulu). And apparently, there are no regular correspondences between clicks in these languages and whatever in their click-less relatives; it seems as if clicks occur only in loanwords from other languages with clicks, or in words with uncertain etymologies. (But I may have missed something; I am no expert in this.)2. Can anyone point me in the direction of articles dealing with the development of click phonemes? Clickogenesis?
This has brought some scholars to the idea that clicks never evolve from anything else, from which they conclude that Proto-Human had clicks and all other languages have lost them. I don't think there's much merit to that idea, though. Just because a particular change has not been observed is no reason to assume that it never happens! I'd personally guess that clicks may evolve from doubly articulated stops involving a velar closure and another closure more forward in the mouth (which are quite common in Africa), which may evolve from clusters, e.g. tk > !. Indeed, I have the idea of an IE language on the back burner where just this happened, such that its words for 'earth' and 'bear', for instance, have clicks.