To be clear, however, when you import images into the Lightroom desktop app they are initially copied into Lightroom's own designated location for the storing of original images, and from there they are uploaded to the cloud. By default, that location is on your system drive inside the local library that Lightroom creates and maintains (it stores previews, local catalog, proxies as well). That local library needs to be kept on the local system drive (different locations depending on your operating system: on MacOS it will be in the users>Pictures library, on Win10 it will be in the AppData>Local>Adobe>Lightroom CC folder), but that copy of the originals can be stored on a different drive as per that Preferences>Local Storage tab.
If you have checked the option on that Local Storage tab to "Store a copy of all originals at the specified location" then obviously that's what you will get. It's a COPY of what's uploaded to the cloud, the master is always the cloud version, but it will be used by the app when editing images using the Lightroom desktop app.
If you have not checked that option, the copy that Lightroom stores locally will become eligible for automatic deletion, but that's not an immediate thing. There are some complex rules which determine when the local copy of any image can be deleted (though even after local deletion it can still end up being downloaded again if you subsequently start to edit it). Those rules means that the "temporary" local copies can linger on your system for months. If you subsequently switch the location of the stored local originals from the default to a separate drive, Lightroom should automatically MOVE any existing locally stored originals to the new location.