Yes, you can easily move a Case File from your iPad (maintaining the organizational structure of your documents, annotations, etc.) to another iPad. You can move the Case File to a USB thumb drive, or connected USB hard drive, or to the built in Apple Files app to move it to a cloud storage provider that also integrates with the Files app.
Your Case File can be stored on Dropbox, or another cloud storage provider, but it needs to be zipped (compressed) before moving it from your local Files app to the cloud storage provider; and then unzipped (expanded) after it is moved back from the cloud storage provider to the local Files app on the other device. You cannot open and work on a Case File while it is stored on Dropbox, or another cloud storage provider.