If you have a taxonomy 'colour' with terms such as 'red', 'blue', etc., then that setting is for whether to allow queries such as
mysite.com/?colour=red or not
The example of mysite.com/?taxonomy=example is fairly meaningless because "taxonomy" is not what is used, it is the slug of the taxonomy that is used (or you can specify a different string in the settings).
When you add URL parameters that WordPress doesn't recognise it will simply ignore them, so if you enter mysite.com/?taxonomy=example, that will give the same result as typing just mysite.com/
In my example I have created a taxonomy "linksammlung" and added a term "super". I can view the archive of this term in the frontend with the URL hidden link. I thought the option "query_var" would prevent this. My goal is to hide all the archives of this taxonomy. The URL should show a 404.
For the query you were describing, i.e. hidden link
then I think the relevant setting would be "publicly_queryable" not the query_var option, but looking it seems we don't include that option in the taxonomy settings.
I haven't noticed that before, so I'm reporting it anyway, just for your information.