No - it's more repetitious, along the lines of

I like pineAPPles, baNANas and MANgoes,
Pineapples, bananas and mangoes...

with the stress on the second syllable of "pineapples" which falls a bit awkwardly. I don't think this song was actually About anything much - maybe that's all I can remember of it because that's all there really was! I prefer yours -

Hey - what about the Chiquita Banana song, anyone remember that? I had it emblazoned on one of my schoolbook protective paper covers, which we all had to use, and those four lines have stuck in my mind long after the book's contents fled to the nether regions of oblivion:

I'm Chiquita Banana and I'm here to say
Bananas give you energy for work and play
And the calories count, I am so happy to state,
In the medium banana's only 88 !

But I had no tune for it, only these words; so I promptly made one up and then proceeded to drive my mother crazy. When I finally heard the real music it was a sad let-down, monotonous and tame. Mine was much better -