The separator item in menu admin is just a logical thing. IIRC, it causes a break when you want to place an option item as a new top-level item rather than under a section.
A standard practice to get the appearance you're describing is to use CSS to put a border-left on all the links, and then use the :first-child pseudo-class to remove the border on the first menu item. A quick Google turned up this example: http://tobto.org/css-design/modern-separators-in-lists-menu/. This may not be supported by IE6 without some extra effort though, so alternatively you can remove the border on the first item by finding its class/id in the page source and targeting it with its own CSS rule.