Yes, They can use FileMaker Pro and Open Remote... to connect to the file or there's an option called Instant Web Publishing (IWP) that permits access via a web browser.
Either approach requires some extra work setting up port forwarding through your internet router. IWP eliminates the need for your other users to purchase FileMaker Pro, but provides a much more limited user interface and you have to make sure none of your scripts use steps that are incompatible with web publishing.
FileMaker offers a 30 day free trial copy. If you haven't already, download it and give it a whirl. You'll be able to experiment with both forms of access using your trial copies to get an idea on what's required.