The study of Proto-Indo-European is considerably more robust than what the other post is making it out to be. We know quite a bit about the phonlology, yes, but also about its structure, syntax, vocabulary, and through these its speakers' ideas about their society: life, love, the physical/spatial world around them, their plants and animals, their concept of self and other, their family structures, technologies, material culture, diet, sense of morality and of restitution, their sense of their place in space and time, their beliefs, their "religion." All academic work is inherently "just a hypothesis," but this particular hypothesis is supported by a veritable mountain of evidence and centuries of careful study and theorizing. Our understanding of PIE continues to grow and important contributions continue to be made, especially in light of new discoveries. The laryngeal theory is a great example.

If a current world-renowned Historical Linguist (like Jared Klein) were to go back in time (and we don't even know what time would be correct, or where), he/she of course would not be able to speak fluent "PIE" like in the movies. He/she would, however, have a very good grasp of the basics and probably very quickly pick it up. The color of the language would depend on the time period, the place, the social situation of the speaker, and perhaps other variables we don't even know about.

PIE is a hypothesis, there’s no writing of it or even records of it, basically no evidence of it other than the fact that linguists can find similarities in the earliest indo-European languages leading them to believe in a common ancestor. So no one would other than the original speakers of it would have any idea of how to properly speak it, modern day linguist can only come up with basic phonetics they believe were present.