As far as I can tell, it stores the files in a temporary directory. This is the output I get when installing a template from the asset library, and then clicking the console (when hitting the X button): erasing C:\Users\Username\AppData\Local\Temp/Godot/tmp_asset_116.zip, so I think it stores the assets in temporary memory and only imports them into a more permanent spot if imported into a project.
That said, I don't know for sure if this is what is happening. Hopefully someone who knows will chime in.