They really wouldn't be able to tell it was "copied".  All traffic to a website
is potentially logged, and if they're actively monitoring it, all they would
see is a GET for every single file on your website in a short period of time,
which might indicate to them that an automated process was used.  But that's
about as close to figuring out someone "copied" their website.  I doubt anyone
would have sophisticated enough log analysis setup to flag that.  I'm sure
your safe..