If the plugin was written prior to v4.2 then it will not add Nav Tabs properly. The code for adding tabs changed in v4.2.
What plugin are you trying to use?
Correct, however, plugins can still add tabs during install
If the plugin has not been updated to do so then no it won't. Many plugins, even one of mine, have not been updated to add the navlink. Just because a plugin can do something does not mean that it does.