Can I assume that when downloading a DB backup file (.sql) it will contain the current content of the site, or is there something I have to do to make it current before I grab the file? I usually work with a different server host and that has the current DB to download.
That will depend on where you download the .sql file from. If you use phpMyAdmin to export and download the database, then the database file you get will be as it was when you exported the database. If you subscribe to our Backup Manager service, those database files will be created at set times. If you have a WordPress site and use WordPress plugins to backup your database, they may vary greatly in how and when they actually create the database backup.
In general though, if you want the latest current version of the database, just export a copy in phpMyAdmin or from the command line so you know you have the latest current version of the site. Hope that helps!