The following section of the Wave whitepaper suggests that the chat app aspect was minor to the project. It was all about solving collaborative rich text editing:
> Waves are hosted XML documents that allow seamless and low latency concurrent modifications.
The following section suggests that the Wave team had a specific goal related to rich text OT extensions, which were NOT trivial at the time:
> There are others that offer rich text, such as Google Docs, but do not offer a seamless live concurrent editing experience, as merge failures can occur.
It also suggests that it was specifically intended to be featured later in Google Docs (it would not make sense to dunk on their own product). It actually doesn't matter if it is the same team or not. It is common to have a dedicated R&D separate from the deliver team for such breakthroughs.
I'm not saying it necessarily wasn't used in docs but it seems like you also don't have any information indicating that it actually was and are just assuming that it must have been, so I would ideally want confirmation from someone who was actually involved with it at Google.
Isn't this just showing that they both used OT rather than that the docs functionality was based on wave? It seems like the version of docs that added this was likely in development at the same time as wave so unless you specifically know that the people who worked on wave then worked on docs I would assume that different people were responsible for it so the fact that they both used OT (which is pretty standard) doesn't seem to necessarily imply a connection.