I don't know whether it does or doesn't, but I just don't see any evidence that demonstrates that we do. E.g. how do you know from your experience whether the verbalization drove the conceptualization or whether it's effectively purely narration of non-verbal conceptualization? It's not even a given that they happen at the same time vs. being a post-rationalization of processes happening separately (e.g. we know from split-brain experiments that the brain halves are perfectly happy to verbalize explanations for decisions they demonstrably didn't make)
I personally have a very hard time thinking out loud but have no problem thinking quietly. I'm for example terrible at explaining something while working on it but could easily explain it afterwards.