Quick related side story: Recently I was with my friend who is much better at Japanese than me. So much so that I won't try in this story to emulate the Japanese he used, because I'd just mess it up.
It was a cold day and we were in a liquor store to buy some ice. We couldn't find as much as we needed, so we asked if there was more in back. The older woman running the shop asked if we were buying the ice "for drinks". My friend replied, "no, I just don't think it's going to be cold enough tonight, so we're going to go up to the roof and throw the ice off."
The older woman replied, "oh, then you'll need more ice."
Not just a successfully executed instance of sarcasm, but also a well received deadpan return on the part of the woman. I laughed. We all knew it was all done in good fun.
The short answer is "yes". A native speaker, and even a non-native, can sell irony and sarcasm in Japanese.
The prevalent belief that Japanese culture and language simply doesn't have it, or that it can only be perceived as "mean" is just plain wrong.
Sure, it can reasonably be said that the degrees to which sarcasm and irony are used are different, but that's only part of the story.
What makes sarcasm and irony work in any language is the context of understanding, which extends far beyond just the topic and words used. The entire context of the interaction matters. The people involved, the time, the place, the feelings present... everything. What I can't convey to you in the story above was the lilt in my friend's voice, the understood nature of the interaction, all the things that can't be written down that make it seem a bit mean in writing but fun in person.
Saying Japanese doesn't have sarcasm is like saying sarcasm can't be written in English. It's not true, but the whole reason for the existence of emoticons is because otherwise it can be more difficult to convey sarcasm in writing. Not impossible, but you can see it takes a higher level of skill to convey sarcasm in writing without resorting to emoticons. Same deal applies when being sarcastic in Japanese.
While some of the time a miss said phrase or poor use of the language can be at fault, it is also just as likely that when a non-native speaker attempts irony or sarcasm and fails, it's not because that form of irony and sarcasm simply doesn't exist in the target language, it's only that they have misread some aspect of the overarching context of the interaction. They weren't as good friends as they thought, the situation wasn't as casual as they thought, the timing wasn't right, or something like that.
It's an error, of course that can happen even between two native speakers, and of any language.
However, because of this persistent insistence that Japanese doesn't have sarcasm or irony, people are quick to blame the language and culture.
There is a phrase in Japanese that applies: 空気{くうき}を読{よ}む
. The ability to "read the air". Having a feel for the context is what drives the ability to say one thing while meaning another.
It is, of course, an art, not a science, so no one can advise you, "do X and you will successfully achieve sarcasm and irony in Japanese."
If you can learn to "read the air," though, you can tell people you intend to go swimming in the Sahara and get the chuckle you hope to get.
Hope that helps.