Nope. Here is a little history of the word pussy. It almost certainly started likening a woman to a pussycat in the 19th century or earlier. The phrase pussyfooting around, which appears around 1900, implied being timid, afraid, like a cat. No sense of woman there.
Pussy was in use in theater circles by the late 1940’s to mean a homosexual male. Interesting how these terms morph from women to homosexual males, much like a faggot.
The term for female private parts came on a separate path when it morphed from the word, poesboekkie to the Dutch poes, which is linked to the word puss.
In this Cruz’s case, the use of the word pussy is the most correctly used as a term for a pussyfooter and at the extreme, maybe as a term for a faggot. No sense of female private parts here and no obscene use here.
I see where you got the etymology from, but I still contend that the two words in this context are synonymous.
I thought a faggot was a stack of wood at one time
No sense of female private parts here and no obscene use here.
the common use takes precedence as to meaning