The intended imagery seems pretty clear to me!
Interesting question, now that I think about it. All I can say is that the lead singer of the band Phoenix is French, but writes lyrics in English that are purposely vague and ambiguous. Thinking about that (he does it in English; why wouldn’t he also do it in songs he writes in French?), I would assume the French would mess with words and have word-salad lyrics in some genres of music.
I would assume that most any culture that is attempting their version of word-salad genres or pun-heavy/jargon-specific rap would have that in their lyrics, too. I suspect the “Kurt Cobain of Serbia/Malaysia/Paraguay” has lyrics that speak to their psychic pain but reference the equivalent of mulattos, mosquitos and such ;). Come to think of it, I hear Latin rap that, from my limited understanding, incorporates all of the rich wordplay of hip hop.
American songs?
For incomprehensible, I present, Robert Plant, “Burning Down One Side”. It took me twenty-odd years to realize he was singing “Try as I might, try as I may”.
I’m not an expert on Chinese genre music, but Chinese pop music always seems to be extremely well-enunciated to me- almost newscaster-like. I don’t have any particularly expertise, but I assumed they was part of the general push in media towards standard Mandarin.
Most responses seem to be talking about intelligibility–recognizing what the words are–but the OP seems to be actually asking about comprehensibility–understanding what the words mean?
ETA: Though Thudlow has the reverse impression. And I suppose it’s too late to focus, anyway.
Yes, I am assuming the OP is asking if non-English songs are written in “word salad” - i.e., jumbles of words intended to sound a certain way, like Lennon’s nonsense lyric for I am The Walrus, or my reference above to Cobain’s Teen Spirit word salad.
Check out how incomprehensible this song is.
Which I’ve heard are the original lyrics.
Speaking of lazy (or maybe stylistic?): Birthday Greetings from Joe Cocker
I assume you mean English-language songs? You would be surprised at the amount of pop music that is in English, even in non-English speaking countries.
For example, here is German producer Schiller performing with Indonesian singer-songwriter Anggun in a stadium in Berlin:
Always You
And in a stadium in Hamburg:
İnnocent Lies
What language to pick? English, of course. And the crowd seems to be into it.
We are probably all aware of certain Weird Al’s song where he mocks certain Nirvana’s song for it’s incomprehensibless (all these marbles in the mouth).
Here in Slovenia we have a similar clown who did very similar gig with certain very popular local band.
So, my answer to original question would be yes.
Obligatory Bloom County Strip
And you would be wrong. 
The entire song tells a true story. And, no, prostitutes were not part of the story.
What I found interesting about the song is that, when young, I found Ian Gillan difficult to understand on first exposure (although by modern standards he isn’t). Then you add to a number of Deep Purple’s songs, lyrics that have quite clear meaning, if only you had any clue what the story they were on about was. Some songs were describing quite personal events, Smoke on the Water the ridiculous story of how they recorded an album under less than easy circumstances. Cover bands the world over would have sung the lyrics to Smoke on the Water, and even if they enunciated perfectly, most people would have had no clue what it was all about.
Which raises the amusing question as to how many cover bands repeated totally misheard lyrics when they performed songs.
IIRC, Icelandic band Sigur Ros performs songs with lyrics that are truly incomprehensible – they’re written in a made-up gibberish language.
When I was living in Japan, I noticed that when there was a musical performance on television the lyrics were often captioned. Sometimes this captioning was my only hint that the lyrics contained English words, because they were pronounced in ways that no native English speaker would pronounce them. But I don’t think this was an artistic choice, the singers just didn’t speak English very well.
I don’t speak Japanese very well, and once asked a friend about the lyrics to a (non-English) Japanese rock song. She listened for a moment and said she couldn’t make any sense of it. She said she wasn’t sure it was even Japanese, and that it might be English-esque gibberish. However, I checked just now and was able to find Japanese lyrics online, so I think my friend just couldn’t understand what the singer was saying.
The Cocteau Twins vocalist Elizabeth Fraser is renowned for her incomprehensible singing. Perfectly enunciated, but sounding like some sort of made up language. But apparently it isn’t. It is perfectly good English with her own variant of how the various components of the words should be emphasised and intoned. I have read one comment by another musician who said that on her music stand are the lyrics written out in perfectly ordinary English.
Cookie Monster vocals in some Death Metal bands is perhaps one of the most egregious forms of near incomprehensibility. They seem to be a great way of covering up for a complete inability to sing.
To clarify, I was referring to the ease or difficulty of determining which words are used in a song.
I thought of this question while listening to the closing song for an anime (Chocotto Sister) while reading the subtitles. I noticed that many words seemed to run together (vocally) and some others seemed to have breaks in the middle.
Here’s a video of the song http://www.dailymotion.com/video/x78tjg_chokotto-sister-ending_creation. For the longest time I heard the lyrics as “suri-ko” and “rori-pe”.
They are words, but not necessarily perfectly ordinary English.
The following is going to sound weird to anyone who is not familiar with Cocteau Twins. So I have to preface it by saying that I think they produced some of the greatest music ever made and no band has since matched them. The music is not as weird as this is going to make it sound.
The first two albums, stuck to more or less perfectly ordinary English. For example, here is the first verse from When Mama was Moth from Head Over Heels:
Sunburst and snowblind
I’d seen the fear running down my brook
While mama was clear, one more brook
Chills all start screaming
Ribbed and veined
The sunburst and the snowblind
A chill of fear running down my brook
When mama was moth, I took bulb form
Body electric
Writhe in vain
Body electric
But starting with the Treasure album, Liz started taking a different turn.
Here’s an interview with Elizabeth Fraser discussing how she wrote the lyrics to Whales Tails on Victorialand. She says she got the words by going through books and dictionaries in foreign languages. She recites the words for the interviewer. She says the words don’t take on any meaning until they are sung.
I think maybe around Heaven or Las Vegas, Liz went back to more Englishy words.
I had to look up the lyrics for this song because I really needed to know if little Hurley Burley was actually giving his anus curly wurly (and then asking if he needed a ride! How considerate!) It turns out the lyric is supposed to be that Hurley Burley came by in his curly wurly but that is clearly not what is said in the song. I expect a deathbed confession from one of the band members that these mondegreeens are actually some deep and committed trolling. Because seriously, the guy on the receiving end of the rimjob should be the one offering to drive.