We could, I suppose, experiment.

But I share your intuition, both that this is probably well-covered in the sociolinguistics literature, and that politeness markers can increase the effectiveness of a communication.

It's also worth noting that what counts as "noise" (in the sense we're using it here, which includes redundant signal) depends on my audience. If I know who is reading my words and I know what their priors are, I can communicate way more efficiently -- I only have to provide evidence for the places where our priors differ. (Case in point: in pretty much any other community, I would have needed to use more words to express that thought, rather than rely on a shared understanding of "evidence" and "priors".)

Anyway, I don't feel like actually, you know, doing research, but I'll ask around among the appropriate cohort of my friends and see what comes up.

ETA: Heh. Your most recent comment said essentially the same thing. Ah well.