Yes they do begin where they left off, but only if they can connect to hosts of the file (people who are sharing the file). To learn more about how to continue files, see
http://www.gnutellaforums.com/connec...889#post139889 .. yes it's old but same principles apply now.
Oh & now you can use the Get More Results option by right-clicking the search tab, which is very handy. The more hosts you find, better chances of getting a file to continue & getting it to download faster.