I am pretty sure that Tableau does track that type of access but whether that gets displayed in the Server UI I'm not so sure. We're on v10.1. I've got a few published data sources that suggest they've had 0 views (hits) and 0 connected workbooks.
I've just connected to one directly via Desktop and one via the web authoring facility. The view count on the Server UI still says 0 BUT there may be an element of caching going on which means this might not come through immediately.
I've connected to the postgres database directly and looked in the _datasources_stats view for the data sources I've just tested. The last_access_time value in that table matches the times I've just tested, and the nviews value (number of times datasource has been accessed) has a +ve number (but already larger than 1, so makes me think the info on the server isn't quite right). I've connected to one of the datasources again on Desktop, and the nviews has increased and time changed. Server info hasn't changed, so I'm thinking that it isn't picking direct Desktop views up....
Looks like your best bet will be to use the postgres database directly to check this stuff out. There's a chance though that the tables I'm referring to might have changed since v10.1 though... This article should help explain what you need to do to open up access Collect Data with the Tableau Server Repository. I typically use a feel tool called pgAdmin to quickly query the tables directly.
Hope that helps a bit