I have one of those, exactly the same. However, rather than drinking the liquid as it slowly leaked, my cup was actually destroyed. Yes, I put it in the freezer to freeze the liquid (which is what you're supposed to do with it, apparently) and the liquid decided to freeze and crack the plastic open. So the cup was basically broken because I followed the instructions properly. Pretty pointless, methinks. I have another one now that I use, but I use it as a normal cup, it's not going in my freezer after what happened to the other one.
On the topic of drinking odd stuff, I actually did something like this intentionally. In my first year of university a favourite drinking game in my shared flat was 'Ring Of Fire'. Look up the rules online if you want to know more, because they're too long for me to be bothered explaining here. Anyway, the glass in the middle, by the end of it, contained a mixture of various lagers and ciders, wine, vodka and various mixtures, sambuca shots, various other drinks including orange juice, chilli powder, chilli flakes, tabasco sauce, and I believe something like sake or soy sauce. Most of the stuff was when drunk people got carried away and decided to add random stuff to see what would happen. It looked completely foul, and everyone who tried any of it thought it tasted vile. I downed it in one go and actually enjoyed the taste, weirdly enough (this was voluntarily too, when the taxi to take us to the nightclub arrived and the 'drink' would otherwise have been tipped away...).