Yes, the maximally concise polite post likely uses more words to express the same number of thoughts than the maximally concise non-polite post.

That said, a typical LW post is far from maximally concise.

The question is, does a typically concise polite post use more words per thought communicated?

I agree with David_Gerard here: if the answer matters, I'd like to see some actual measurements.

Conversely, if we don't care about the measurements, maybe the answer doesn't actually matter.