Not with the "core" navigation providers (without some "tweaks").  They go through and check whether the person has access to view that tab or not and, if not, don't even show the tab at all.  However you could *cheat* by hiding the page from nav (so don't "show in menu"), and then manually adding a page which links to a URL and then enter the URL for that tab. 

In other words, I'd add a page, but then in page settings under advanced settings, change the "Link Url" property to "URL" and then enter the url to that page.  Additionally make sure it is visible to all users (so it shows in the menu).

Now what will happen is it will always show in the menu but when it redirects somebody to that URL it will say "oh crap, these people don't have rights to view this page" and then it will redirect them to the login and set the redirect url back to the page you tried to send them to; they log in and then they go back to the page you wanted to let them in to.  Beauty.