Just like Eric above has said it's not uncommon in anime, so is in the manga world. The translator 'localized' the joke. Well 'localized' is just a word I choose though.
In my country whose language ain't English, many mangas from Japan are published, but as far as I remember, I can't remember a joke appeared in Japanese. Once I read Miiko (I forget it was in Kocchi Muite! Miiko or Miiko Desu!). The setting was in the bus, where one character named Mari have a car sickness. Then, Miiko engaged her classmates to play a chain-word game (where someone says a word and next person has to said a word started with the same last alphabet as the previous word spoken) so that Mari would forget her sickness. Too bad though, accidentally, the words their classmate said all had relation to the sickness, like food's name (imagine you're queasy and have to be reminded of food), even one clearly said "puke" XD. Miiko manga is from Japan, so were the words I read in the chain-word game in Japanese? Nope. They're in my native language. But the translator did a very good job in choosing the words, so the story ain't disturbed even a little.
Another side is from manga scanlation world. Many scanlations have something like "TL's note" (Translator's note). There, I often (not that often though) see translator told how hard it is to translate the joke, since it's a wordplay like the tongue twister Eric gave as example. Some tried to 'localized' it, some left it as it is, wrote the literal meaning, and later gave explanation about the joke.
I didn't read Bakabon, but yeah comedy/gag manga usually will have many words-play like that. I don't really know since I'm not a translator either, but translating joke must be very tough, because you have to keep the meaning intact, while keeping the joke itself.
So, yeah, Bakabon IS originally in Japanese, and all the puns you've seen is originally in Japanese. IMHO, with Bakabon you read that made you even questioning the origin of it, sounds its translator did a very good job with 'localizing' the jokes :) We don't know whether the meaning is intact or not, but I think as long as you read it and you don't feel something's lost, well we could say it's very good :)