I realized this is not entirely obvious from the documentation.
When I search for something in the Dash, a UUID and a search phrase is sent to productsearch.ubuntu.com, providing the Smart Scopes service. If I then act upon one of these results, then that is reported along with the UUID. This is fine.
However, what if this search results in a local file and I click to open this file. Is that action too sent to the Smart Scopes server, or does that only apply to results that actually came from the Smart Scopes server?
And I'm happy too answer my own question on this one. I asked Michael Hall from Canonical and he confirmed that they will not see which file I clicked on, but only that I activated something local.
That's good. It was really the only uncertainty I had about Smart Scopes.