No...I don't think so.

As you said, Kaufman's humor was entirely different from most other peoples.

Here the "joke" is in the fact that Kaufman's "role" is highly specific.

The only act he does is when the words...

Here I come to save the day!

...are heard.

The rest is in his anticpation of the line coming, his preparation for his performance and his gusto during his one job.

The rest is pure performance in the vacuum.

He could have done this to pretty much any song....and that's why it's genius.

Here's something that covers it...which I found after I wrote the above..

Andy takes the stage at Saturday Night Live’s Studio 8H and starts the audio recording of the song. Watch how he waits a beat. Then, listen carefully—the first laughs start at about 10 seconds in, and on first viewing, or even second viewing, it feels like Andy hasn’t done anything to earn the laughs—yet. No performer goes on stage and does nothing, but that’s exactly what Andy does. Just watch. He stands there. The song plays. He waits. The audience waits.

But really, Andy was doing something. He was a master of subtle facial expressions: Notice how he switches from blinking his eyes rapidly to holding long periods of focused eye contact. Notice how he looks confused, which confuses the audience, which is exactly what Andy wants. Look at Andy twitching; his fingers curl and stretch, back and forth, by his side. He’s uncomfortable, nervous, like it was his first time on stage. This helps Andy’s performance, because at 15 seconds in, when he pretends to sing the first “Here I come to save the day!” the surge of laughter breaks the pent-up tension he built up in the room.

The genius of Andy Kaufman is what happens at 30 seconds into the performance. Andy knows the crux of his bit—pretending to sing “Here I come to save the day!”—is now given away. Andy was a master of comedic timing. He knows he needs to rebuild the tension of the performance to deliver more laughs. So to do this, watch how Andy briefly lifts his head and opens his mouth to make it seem like he’s about to sing again, but then puts his head down in shame after he realizes, and the audience realizes, that it’s the wrong part of the song. It’s perfectly timed, obviously rehearsed. During a single performance, Andy invoked from the audience not just laughter during his singing, but also confusion, frustration, and wonder at everything that happened in between.

^source

You don't need to know anything about MM, but... cultural context always helps in humor. In this case, it's that that MM was an American 1950s hero cartoon, and thus had a suitably heroic song.

He chose this song to work his magic, because it's dramatic. He could have chosen other songs, but an angsty folk song by a failed poet wouldn't have the proper contrast against his bumbling.