No, for two reasons:-
You'd have to enter a password on the server to copy a file to the client - not possible in an automatically run script. The client can't be 'seen' by the server (when connecting from 'out there on the internet' anyway) so there's nowhere (DNS'wise) to send the file to.
Ah, ok. I was thinking with ssh keys installed to connect to the other machine (laptop in your case?). I run duplicity to a remote machine that changes IP, but is always accessible- using ddclient in my case but could be anything. The server machine runs the script, scp's the files across and closes the connection without the need of password authentication.