Well, it does work if you're trying to say that something's really really unimportant. Then, no matter how hard you try, you'll find it impossible to underestimate its importance, because it's so unimportant in reality. But what people usually mean when they use this phrase is the opposite of that: i.e. that the thing is so important that it's importance can't be overestimated.

Maybe what confuses the issue is the apparently-similar phrase, "The importance of X should not be underestimated."