Yes.
Too lazy to look up an actual cite, so here’s what AI says:
Birth of “Boonies”: The clipped form boonies emerged as military slang in the 1950s and gained widespread popularity among U.S. troops during the Vietnam War to refer to the remote, dense jungles and rural countryside outside of urban hubs like Saigon.
I live "in" the actual boondocks.
Down, under, into, over at…it all sounds like home to me. 
To my mind, “down” implies specific relative geography that I don’t associate with the boondocks. “Out” is where the boondocks are.
The boondocks are down by the bay where Bumfuck, Egypt is sited.
I’ve always said “out in the boondocks.”
One of the defining features of being out in the boondocks is, when asking one of the locals for directions to somewhere else, the response is “You can’t get there from here. You have to start from somewhere else.”
“And when you get there, turn left where the drive-in theater used to be.”
If you put these two songs together, it paints a picture of them being set in San Francisco. She lives in a fancy house up on Nob Hill. Meanwhile he’s down at Fisherman’s Wharf, sittin’ on the [boon]dock by The Bay.
We’re all overlooking the second line of the song.
“People put me down because that’s the side of town I was born in.”
By definition the boondocks is " a remote, thinly settled rural area." It can’t be the wrong part of town, because a town is not “the boondocks.” It doesn’t matter if it’s uphill or downhill from the boss-man’s house, it still isn’t part of town.
A far more geographically appropriate set of lyrics would be Lefty Frizzel’s Saginaw, Michigan. That song, which predates DITB by only a year, places the poor but honest son of a fisherman living on the shore of Saginaw Bay, a few miles away from Saginaw proper, where the greedy, snobby father of the girl lives.
But that would put the singer on the dock of the bay, which creates another dilemma.
Now, you’re just wasting time.
Seems pretty evident the lyricist did not know the definition of “boondocks”, or just liked the sound of the word and figured nobody would notice.
IOW: “It ain’t that kind of song Kid”
I think that, even if he did know the meaning of the word and had heard the phrase “out in the boondocks”, he would have correctly figured that “down in the boondocks” is a better lyric to sing.
Out.
Surely there’s a country tune I haven’t heard yet where the singer is “down and out in the boondocks”…
Hey, then they could make a sequel to that 1986 Nick Nolte/Richard Dreyfuss movie classic,“Down and Out in Beverly Hills”. How cool would that be! 
A little history about the word: It apparently was mostly used by the Marines, supposedly having picked it up in the former US territory, until after WW2, and then started creeping into the popular lexicon. I guess former Marines might be familiar with the Parris Island area called “The Boondocks,” made infamous by the case of Sgt. Matthew McKeon in 1956.
But getting back to the OP, nah, I don’t think it’s ever been used with any consistency to refer to the “poor” or “bad” side of town as the song indicates. Typically just means “way out there somewhere.” So far as “down” versus “out,” well, in the song his girlfriend and her dad, his employer, do live on a hill.
Nob Hill in San Francisco.
Joe South never lived in San Francisco. More likely, Buckhead in Atlanta or Hillwood in Nashville…or just a writer’s imagination.
How many boondocks can one poor down-and-outer live in (or sit on) at one time?
I’ve lived in (and sat on) several boondocks in my life – but only one boondock at a time.
Ah, but boondocks are never found as a singularity. If you actually find yourself in one boondock, you are totally surrounded by more boondocks. You may have one particular spot you claim as yours out there in the boondocks, but the rest of the boondocks are still there.