In my first answer above I didn't see one short visit as reason enough to start learning a whole new language from A to Z, but in the same message I also wrote that learning
some elements of the language would be a good idea. And if you actually get infatuated with a language and a culture during your visit then that could of course be reason enough to continue to study it, but now with the goal to learning it as more than preparation for just one specific trip.
That being said, I have in at least one case done a little bit more than learning a few touristical phrases by heart, namely in 2006 when I bought a trip to Cabo Verde. The problem was that the flight only took me to a flat and boring island named Sal, so I contacted a local travel agency to organize a trip to two other islands. And because I wouldn't have a guide I thought that it might be prudent to learn a little bit of Portuguese - and when I got to Cabo Verde less than a month later I could have short conversations in Portuguese (with some Spanish vocabulary to fill out the holes). And when I spent 5 days in Maputo in Mocambique half a year later I could speak Portuguese quite fluently and only switched to English when my hotel tried to kick me out of my hotel room because my Danish travel agency had made an error.
So in this case I did actually get something out of learning the fundamentals of a language for a one week trip, but for my trips to Asian or African countries I didn't do the same thing - I just learnt a few basic words and phrases (plus a lot of geographical and cultural stuff). However I also brought home various dictionaries and other books as souvenirs from those trips, and some of them turned out to be essential for learning or refreshing a couple of other languages. For instance my one and only Indonesian dictionary was bought in Manila.
In June 2008 I did something similar: I wanted to refresh my Romanian before a trip to Romania and Moldova, and during my preparations I accidentally hit upon the HTLAL forum - and got hooked on language learning...