It is not true. You will see the analytics code flash in the URL bar as soon as anyone lands on the page!
It not possible my dear...the google crwal machine will track all the sites in some period of time so be patient...and check once again..!!
No, Google Analytics will track all human visits if installed correctly. Either it is not installed correctly, those keywords get no search volume, or you are wrong about the position they have in serps (i.e using a browser that is showing personalised results.)