No. In fact, it’s not even necessarily about language; “translation” can mean other things besides converting information from language to another. Language is just one barrier to humor, though a common one (and particularly daunting in the case of puns). The larger topic is humor that works in one culture, but not in another–even if the two cultures share a language.
I have argued in the past that most forms of humor rely largely on surprise. It’s a response to confounded expectations. Of course, that requires you to have those expectations in order for the humor to work, and many of those expectations are products of the culture we live in.
Take, for example, the rather strong American taboo against public nudity. The existence of that taboo makes public nudity a strong focal point for potential humor–streakers, skinny-dipping mishaps, locked out of the house scenarios, and so forth. To a person from a culture with less strict standards on public nudity, some or all of those would lose a lot of their humor.
Say you have a skit about a yokel come to town, who is accustomed to skinny-dipping, because there’s never anyone around the places where he swims. The hotel he’s staying in has a jacuzzi. Eager to try it, and with no one around to demonstrate proper etiquette, he strips down and climbs in to soak. Other people arrive, and shock and shenanigans commence because he’s naked.
Japan, on the other hand, has a tradition of public baths. A nude man soaking in a common pool of hot water is not outside their cultural expectations. Our yokel may be (and, indeed, almost certainly is) breaking some other elements of the etiquette they would be familiar with, but that wouldn’t be the focus of humor in an American skit on this theme. As a result, at least some of the humor would be lost (or redirected–“look at the silly people freaking out over a man bathing”) if the skit were shown to a Japanese audience. The humor doesn’t translate very well, and it has nothing to do with the language barrier.
I think humor breaks down into a number of categories for translation purposes, each with their own challenges. The list that follows isn’t exhaustive, just some ideas I have along that line:
Physical humor. As far as I know, there is no culture on Earth with a hallowed tradition of slipping on banana peels, so no one has a subconscious expectation of pratfalls. As a result, they tend to translate well.
Body humor. Everybody farts, and it’s generally considered unpleasant. Most cultures have at least some general expectation that people will try to keep unpleasant bodily functions away from others. Body humor is often translatable.
Tales of woe/rants. Most people, regardless of culture, have some sense of probability. One unlikely mishap can happen to anyone. Two in a row is just an unfortunate coincidence. The longer the chain gets, though, the more improbable it seems that someone would have an unbroken string of bad luck–and the next misfortune subverts that expectation. This kind of humor can translate, if the individual mishaps are sufficiently unexpected in the audience’s culture as well.
Humor based on behaviors or taboos specific to a culture. These don’t translate well at all. They can be made to work if you introduce the expectation well before the joke (so it doesn’t feel like you’re explaining the joke), or if you come up with an equivalent situation in place of the original joke. An example I once gave involved a cook waiting for people to leave so he could grab a bowl of rice they’d left sitting on a ledge with a couple of sticks in it. The idea that he’s stealing an ingredient to prepare for his customers is a little off, but you don’t get the real subversion of expectations unless you recognize that he’s stealing a funeral offering. To make it work for, say, an American audience, you’d either need to establish that earlier or rework it as a florist lurking outside a cemetery.
Absurdism. This is really difficult to translate, and just flat doesn’t seem to work for some cultures at all. It’s not a problem with presenting something unexpected–absurdist elements themselves are pretty much universally unexpected–it’s making the jump from “weird” to “funny”. To some extent, one expects people from other cultures to do “weird” things, wear strange clothes, and have different customs. That creates a hurdle absurdist humor has to clear–people have seen pictures of apparently earnest Americans wearing giant wedges of cheese on their heads; what’s so much stranger about seeing one wear a duck? Thus, people in another culture may find absurdist images funny, but not necessarily for the original reason.
Pure wordplay/puns. This is the most language-dependent form of humor I can think of. It usually works if the cultures share the language, but even an accent can ruin it. When there’s a language barrier, the best you can usually hope for is to come up with an equivalent in the target language, like RivkahChaya’s example from Alice in Wonderland.