When the Photos library references files on external media, is the library still browsable, and are the thumbnails still visible, when the external drive is not connected?

Now I have the follow-up question if there is a way with the Photos app to import pictures from SD-Card or iPhone directly to the external drive,

Yes, you can do that. Use Image Capture to import directly from the iPhone or a card - you can select the folder where you want to import the photos to. This folder can be on an external drive. Then importune photos from this folder to Photos, and you can import them referenced, if you do not mind, that referenced photos may be giving you a lot of trouble afterwards.

You will be able to see the thumbnails, add titles and keywords, but cannot sharer edit the referenced photos, if they are offline.