The content project doesn't use CopyFilesToOutputDirectory, but it does support "Copy Always" and "Copy if Newer" on files in the project. The content project doesn't really use the OutputPath property, so it leaves copying source items up to the parent project. This is done by the parent project invoking GetCopyToOutputDirectoryItems, and adding the outputs to its own list of files to copy to the output directory.
To get a list of the files that would be copied, make your target depend on the AssignTargetPaths target, and use the ContentWithTargetPath and _NoneWithTargetPath item groups that it creates. That will be the list of files that would be copied, if we were to copy them.
It's up to you if you want to copy them somewhere before zipping them, or if you can just pass the item groups as they are to your zip task.