Cloudy's very essence is that it is cloud-dependent, so the concept is "automatically importing to the cloud" and having photos available everywhere. You can switch off syncing, but that's more like pausing. If you enable settings to store locally, that's just a cache for originals which will be put in the cloud.
No. If you want to use an external drive to store your photos, then use Lightroom Classic. You can use Classic to selectively sync images giving you access to view and edit them online or from mobile devices. It sounds like this is what you want.
You need to understand that Lightroom Classic is not the "old" Lightroom, the "has been" Lightroom that is being replaced by the "new" Lightroom. Lightroom for the cloud is a different program for a different user with different needs. If you want your images on a local hard drive, controlled locally, and you have the choice over which images are sent to the cloud then you really need to be using Lightroom Classic.