Q:

Does the "elbow-handshake" have any relation to the phrase "rubbing elbows"?

This is probably answerable with a general reference (or a pair of such references), but I have not been able to find one. 
Etymology Online does not cover the origin of "rubbing-elbows" as meaning to socialize or mingle in a crowd in either the section covering rub or elbow. Other top search hits just cover the meaning of the phrase in discussions of synonyms for socializing (hob-nob etc.), without going into the history and origins.
There is also the "elbow-handshake" (or less formally the "elbow-bump"), where literally rubbing elbows or forearms substitutes for a handshake greeting. Wikipedia traces this to a leprosy outbreak circa 1970 (in Hawaii, among peoples whose primary language may or may not have been English), but is very light on references. I first recall hearing of this handshake from watching a documentary about one of the 1990's Africa Ebola outbreaks, where it was presented as a de-facto greeting replacement that crossed cultures, creeds and nations.
My questions are what is the origin and time period of the phrase "rubbing elbows"? And does the practice of greeting with elbows or arms instead of hand have a more definite origin? And if so, is there any evidence that it was adopted with any conscious awareness of a literal acting out of a the common idiom "rubbing elbows"?

A:

The OED has a quotation for the phrase dated 1750:

Mr. Puff..has wrote a Panegyric on the Occasion; but then he and I have agreed to rub Elbows. [Midwife Pref. p. iv]

So between that and Google Ngram, it looks clear that there is no relation with the infection-control practice!
Interestingly, OED has an earlier quotation (before 1732) for a phrase which is clearly related, and which is more familiar to me as a Brit:

They are all members of Christ, of the blood royal of heaven, even those of them that some would disdain to rub shoulders with. [T. Boston Illustr. Doctr. Christian Relig. (1792) II. 129] 

