[Edited: The Oxford English Dictionary says that to pony up simply comes from pony, so Colin informed us. That means Etymonline's etymology is highly controversial. Edited again: The noun pony has been used to mean "£25" since at least 1797, according to the OED. To pony up has been used to mean "to pay up" at least since 1824 in American slang, says the same dictionary. Is there a connection between English and American slang?]
Assuming that Etymonline is correct, which is now doubtful, the answer would be: yes, these expressions share the same root, which is Latin ponere, from the Proto-Indo-European root/reflexes *apo-, po, ap-u, pu, "(away) from, off, out of".
However, because to pony up apparently came from the first verse of the Psalm that happened to be sung on a certain pay day, the link in meaning was severed there: in the Psalm, the word pone is used in the sense "provide me with / explain to me the law by which I may lead a good life", i.e. it is an abstract word, not at all connected with paying money in that context. If the first line had been O Domine, viam iustificationem michi pone legem, or something else, the slang term might have been "Yo, dude, o domine me now, or I'll take your wife". I have actually no idea how this slang was used in the 19th century, but you get what I mean.
Even so, it is possible that the use of legem pone to indicate paying money would have died long ago, had not the association been felt between "putting down money" on one hand and ponere, "to put down" in standard Latin, on the other. That would be very hard to prove or disprove; I have no idea.
The best treatment I know of is by Raymond Williams as part of his entry on “Realism” in Keywords: A Vocabulary of Culture and Society (page 259), which I have excerpted below.
It is from [old French] real, [to the late Latin] realis, from [the ultimate traceable (Latin) word] res — thing. Its earliest English uses, from C15, were in matters of law and property, to denote something actually existing. There was a connected and persisting later use for immovable property, as still in real estate. The sense of something actually existing was transferred to general use, from lC16, in an implicit or explicit contrast with something imaginary: ‘Is’t reall that I see?’ (All’s Well That Ends Well, V, iii); ‘not Imaginary, but Reall’ (Hobbes, Leviathan, III, xxxiv). But at the same time there was an important sense of real as contrasted not with imaginary but with apparent: not only in theological arguments about the ‘reall presence’ of Christ in the materials of communion, but also in wider arguments about the true or fundamental quality of some thing or situation — the real thing, the reality of something. This use is still very common, if often not noticed as such, in phrases like ‘refusing to face the real facts of his situation’ or ‘refusing to face reality’. Since the use to indicate something tangible, palpable or factual was also strongly continued, it can be seen that there is almost endless play in the word.
Best Answer
The Greek root words in sycophant are sukon and phainein, the latter meaning "to show".
Your words are indeed related by this root word, as are fantasy, phenomenon, diaphanous, emphasis, epiphany and others.