It would be pretty straightforward:
Where you have <!--System:Menu:Resources-->, simply change it to this:
<!--System:IfRank:X-->
<!--System:Menu:Resources-->
<!--System:EndIfRank-->
Replace "X" with the RankID if the minimum Rank (You can get this from Admin > Ranks)
Also Chops I think this would be a sweat addition to the Basic Menu Administration options. Make a couple of check boxes as follows:
Menu Item is visible to Rank <drop down for ranks> <> and above or <> and below.
This way people could hide a menu item like the Online Application when a Member is logged in but saying to make it visible to Everyone and below (obviously there is no one below everyone so this should hide it from members that are logged in). And thus people could hide links like the Gallery from non members by simply clicking the right options on in the basic admin menu. You could also tweak the Static Menu and Content are to work the same way. Currently it only supports Rank and higher not Rank and lower.