Sure they can Andy. Should not conflict with one another at all. Something is going on with Awstats. Might want to try just turning it off and back on again. That works with many things in Hsphere. If that doesn't do the trick then I'd suggest submitting a support ticket.
Getting the same problem. The AWStats directory is in the root, but page not found errors now, even though it has been working for months... Time for a ticket, methinks.