Probably the other way around. PIE's linguistic influence can be tracked based on shared nouns for universal objects. Words for "tree" are going to be fairly easy to track no matter where the language goes, but words for specific types of tree have to be invented based on where settlement lands. The further out you go west from the Aryan diaspora, the less PIE declined words there are.

That said, PIE is not an exact indicator. It's usually best used in conjunction with mythological constructs as well. You can track direct translation of the Sky Father character no matter where you go in Northern Europe, tied to foundational myths of Shiva. You can then also get really nuts and connect Christ to Krishna but that's some Blavatsky shit.

So more of a billiard ball thing, where the Kurgans (or whoever) got their immediate neighbors hooked on milk and PIE, and those neighbors got their neighbors hooked on milk and PIE, and so on?

I was studying linguistics in college until they made me take a Shakespeare course and halfway through the Histories I had a breakdown and changed my major to art. The school treated linguistics as an offshoot of literature, not its own science.