Just move your entire Drupal root somewhere else, and put something else in its place (with a "Be Right Back"-message) while the upgrade goes on.
For instance, if your Drupal root is
/var/www/html, prepare a directory named
/var/www/brb and put a static
index.html-file in it with your BRB message.
Then execute the following pair of commands:
mv /var/www/html /var/www/pending_upgrade
mv /var/www/brb /var/www/html
Now, make sure that your ftp job puts the files in below
When done, restore your site with the following pair of commands:
mv /var/www/html /var/www/brb
mv /var/www/pending_upgrade /var/www/html
The above assumes that you have CLI access. If you don't, most ftp tools have built-in commands to move directories around.