Of course. One example is very well described in the short story by Ted Chiang, on which Arrival is based. It's a fascinating story and well worth a read, whether you are interested in linguistics or not.
And it's not said we could communicate with aliens, it all depends if we are able to perceive their language.
All I'm saying is that the fact two people don't share a common language doesn't mean they can't learn each other's language. That was more an answer to the question asked in the sibtitle of this article than really adressing the hypothetical meeting with aliens.