Is my web hosting company's "Full Backup" sufficient protection before an update? I'm learning how to work my little Drupal site, which is currently hosted on HostGator. It's well past time to update, and I want to make sure I'm safely backing up my site.

HostGator can facilitate "Full Backups" of my files, which they describe thus: 

A full backup includes all of the files in your home directory, your MySQL databases, and your email forwarders and filters. You can back up your account to preserve your data, or to move your account to another cPanel server.

Thank in advance, and/or apologies if this is a crap question.
You need two things to restore a Drupal site: A copy of the database and the folders that hold Drupal. 

I'm not familiar with shared hosting, but I'm guessing that Drupal is installed in your home directory as opposed to /var/www or /srv/www. 

That means a full backup does give you everything you'll need to restore Drupal. Make sure you know how you'd restore it though. No point backing up if your not sure where the files are and how to restore them.

If you want to extra safe or do it yourself, install the Backup and Migrate Module, make a backup and make a copy of your Drupal root directory. (That's the one with sites, includes, themes etc. in it). 

Then if you want to restore Drupal. Delete the bad Drupal root directory and put your old drupal root directory back in. Install Drupal as normal, enable backup and migrate module (it'll be there because you've put in your modified Drupal root folder) and then restore from the Backup and Migrate backup.