"Priming" covers a lot of ground. At one end of the spectrum, there are fairly straightforward lexical priming effects. You can recognize the (scrambled/faint/etc) word "Banana" faster if you've been previously primed to think about fruit. These effects are pretty robust (at least as far as I know) and are fairly consistent with some models of memory.

At the other end of the spectrum are these embodied cognition experiments that fall back on "priming" as an explanation. For example, people allegedly walk more slowly after being primed with words related to old age, or view others as being more "warm" if the subject hands them a hot beverage. These typically do not replicate well and tend to fall back on vague, handwavey theories.

Any worthwhile scientific study is going to consist of highly controlled experiments that are designed to answer very specific questions.

To apply research results to negotiation/persuasion scenarios "in the wild" would be intractably difficult because the situations are going to be utterly uncontrolled.

By the same token, I don't think that it's reasonable to dismiss "priming" as a practical business communication tactic just because it isn't easy to perform a repeatable experiment about it.