Is language externalized thought or is thought internalized language? I believe the latter is much closer to the truth.
Without being a doctrinaire Whorfian, I think it's undeniable that the language we think in to some extent channels our thinking processes. It may be possible to say anything in any language, but what's important is what your language FORCES you to say. Human languages are (pace Chomsky) so incredibly diverse in this (even though I believe they may have historically developed from a single "Proto-World" language) that it's hard to imagine an alien language not being considerably more different.
To the extent that we could never understand it? I don't know. That would depend on what we meant by "understanding." I certainly think we would have trouble appreciating each other's literature. Even in Greek, an Indo-European language, I'm having an incredibly hard time with quantitative verse!
I think basic communication would be possible, however, with any species sufficiently tied in to the real universe to develop the technology that allowed us to communicate. While we're on science fiction, though pre-Star Trek, H. Beam Piper's "Omninlingual" (available at http://www.gutenberg.org/etext/19445
) argues that common scientific knowledge would be the Rosetta Stone that would "crack" a (dead) alien language. (But read also "Hellspark" by Janet Kagan!) I agree this might lead to a basic practical understanding, but could a true meeting of minds be based on that? I don't know; it's fun to think about, though. Thanks for bringing it up, Rameses!