Actually, you can join overlapping points. I do it all the time with dielines, as they come from the engineers as separate lines. Just select the lines that make up the shape you want to "join" and command+j. Sometimes it's tricky, depends on the direction of the lines and such, so sometimes you have to select a few pieces, join, select a few more pieces, join. Depends I guess on how the items are layered.
Check it out. Here's the info from the help files (I searched "join paths"):
Join two or more paths
Illustrator CS5 provides the option to join two or more open paths. To join one or more open paths, use the Selection tool to select the open paths and click Object > Path > Join. You can also use the keyboard shortcut Ctrl+J (Windows) or Cmd+J (Mac).
When anchor points are not overlapping, Illustrator adds a line segment to bridge the paths to join. While joining more than two paths, Illustrator first looks for and joins the paths that have end points stationed closest to each other. This process is repeated until all paths are joined. If you select only one path to join, it is converted into a closed path.
Note: In this process, you may lose complex aspects of your art styles.
The output path has the appearance of the topmost path in the selection.
The join option only results in a corner join regardless of whether you select anchor points to join or the entire path. However, for overlapping anchor points, if you want the option to select a smooth or corner join, then use Ctrl+Shift+Alt+J (Windows) or Cmd+Shift+Option+J (Mac OS).
