Is it possible to play Starcraft 2 at an Internet Cafe without a licence?
Solution 1:
There are 'guest pass' brochures that come with a copy of Starcraft 2 for just this purpose! Typically I believe they last around 7 in game hours or 14 real-time days, providing you a good opportunity to get addicted. If you have friends that have the game, ask them to give you one of their invites, if not I'm sure you could find one for virtually no price online.
Here are some for a dollar on ebay
If the Internet Cafe has Starcraft 2 already installed, you can also select 'play offline' from the login menu. This will give you access to the single player game.
Hope this helps
Solution 2:
Even though you can't play multiplayer, the copy of starcraft 2 at the internet cafe should still allow you to play the single player mode in "offline mode".
If you're just interested in determining whether or not you like the game, Single Player is probably a good metric for that (though it features several aspects that don't carry over into the multiplayer portion of the game).
Solution 3:
Did you speak with the people running the place? I imagine they must have registered the CD-key to some account, with the intention of allowing their customers to use it..