In order to answer the plausibility question, more information is needed. For example, how prevalent are these phonemes in other languages? Basing such a universal theory on one language only (English) is a bit shaky.

Other than that, I would vote for the syllable "ma" as having near universal incidence. Interestingly, many words for "mother" begin with it.

"Jack" is a nickname for "John", a name so common it's used to "identify" unidentified males. I did find this one reference:

"Jack, for instance, was originally from the name Jakin, a corrupted form of Jenkin (John+kin)."

The implication is that the origin of the name Jack, at least, lies in the evolution of words meaning the relatives of John. Interesting also is that the name "John" is featured in several male sexually connoted words or phrases, i.e. "John Thomas", and the customer of a prostitute.