It's doable. Check out Import Records--which can be performed manually or via script.
You can send your managers out with a computer, an iPhone or an iPad with an empty copy of a filemaker file loaded on it. They collect the data in this file and then you can use import records to pull that data into your database.
Import records can add new records, update existing records or both. It has a lot of options and can produce profound changes to the data in your file which cannot be undone, so read up on the process, make lots of back up copies and test things thoroughly before going into production.
Don't hesitate to post back here with follow up questions once you've researched the basic concept.