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No. This requires modifying your site's files (configuration.php) while taking a backup. Backup software must not change the configuration of the system being backed up. Also, during restoration, if you expect visitors to come to your site Joomla's off-line mode is a terrible idea for reasons I have explained seven years ago. What you can do is right after restoration log into your site and set it off-line.

Also note that I understand your misconception that having the site "off-line" will prevent any visitors from seeing something broken. That's patently false. While the archive is being extracted your site is in a "confused" state. Visitors will see something broken. While you are running the restoration script (actually: while the installation folder exists on your site) your visitors will be redirected to /installation/index.php and see the restoration script (that's how Joomla! works, you can't change it without a core hack). So those ten seconds to log in to your restored site and set it off-line is nothing compared to how much time your site would anyway ignore the off-line mode. Use Kickstart's stealth mode to prevent users from accessing your site while you are extracting the backup archive and restoring the backup.

Moreover, I would argue that if you routinely need to do this because the restoration breaks your site you are doing something wrong. You should practice restoration on copies of your site to make sure that the restoration results in a working site in the least possible amount of time. We launched an entirely new site with 5 seconds of downtime two weeks ago. Getting there required just over 3 days of planning and testing.