You can add your own aspx page to the admin folder and bypass admin. Don't inherit anything and then check that they're logged in:

if (Sitecore.Context.User.IsAuthenticated)

Really wouldn't recommend doing this though, as we most things in Sitecore... just because you can doesn't mean you should. Probably best to keep admin pages for admins

You can add your own aspx page to the admin folder and bypass admin. 

Don't inherit anything and then check that they're logged in:

if (Sitecore.Context.User.IsAuthenticated)

I wouldn't recommend doing this though, just because probably it is best to keep admin pages for admins.