Yes, the rest of Eliezer's point holds; that would be why I didn't criticize the rest of Eliezer's point.

Different people think in words to different extents. (And for some of what seems like thinking in words, perhaps the word-generation is more or less epiphenomenal -- though I'd expect it always has some value, e.g. in helping the short-term memory along.) I find that I use words in the same sort of way as I use diagrams or mathematical symbols: as a way to avoid losing track of what I'm thinking, and to enable some degree of rigour when it's needed.

Yes, there are situations when talking to yourself can usefully be considered "communication between two people", but those aren't the situations I had in mind.