What is the maximum number of pages allowed on a Google Site?
From the Google Help document you reference, it states:
Pages per site: No set limit (see note below)
By thousands, do they mean 1000 or 10000 or somewhere in between?
I would interpret "thousands of pages" as somewhere in between 1,000 and 10,000. More than 10,000 pages and it would be "tens of thousands of pages".
Has anyone created or has any example site where this threshold has been tested?
The problem with this is that it would seem to depend on the nature of the site. There is no one-size fits all. As per the above Google Help document, they recommend:
...disabling dynamic sidebar elements such as automatically organized navigation and recent site activity.