Hello Gabriel,
It should be possible to move all the files to Amazon S3 storage but it is important to note there are a few downsides in the process as well.
First of all, you could copy all the files you want to move to the corresponding bucket in the storage which should ensure system would look for and retrieve all files from the storage instead of a local file system. However, I would also recommend that you delete the files from your local filesystem afterwards because it might cause some conflicts in specific scenarios.
The downside is the fact that Amazon S3 storage does not support some special characters so you might need to adjust file names manually which would mean the references would need to be changed accordingly.