Not automatically. You have to set up your own back up system for such and all developers should make frequent backups during development and should set up an automatic back up system for their users once the DB goes into regular use.
If you use FileMaker Server to host the file, you can schedule backups on a nightly or even hourly schedule.
If you use just FileMaker Pro, you can create a fairly simple script that saves a copy of the current file at the time the file is closed each night or on a regular interval.
Here's a link to a thread that spells out an automated backup set of scripts that can back up your file every 15 minutes that I use during development of my databases: Saving Sequential Back Ups During Development
In all cases, backups should happen on a regular interval, be automatic, and the most recent backup should not overwrite the previous backup, the system should be set up to keep multiple copies of your database as sometimes a problem with the file may not be discovered the day that it happens. This not only protects the data from possible file corruption but enables you to restore changes made to the data or system design that you then realize that you shouldn't have made. ("I deleted the contact record for John Doe and now I need it back....")
Thank you SO much but pardon my ignorance - are these Applescripts or Filemaker scripts within filemaker?