I'm not talking sleep mode, I'm talking completely shut down. Would I have to start downloading from the beginning?
If the Nintendo Switch is completely shut down, it will not continue downloading games or updates.
When this happens, your downloads will pause. When you are able to resume the downloads, they will resume from where you let off; you will not need to completely redownload them from the start.
Alternatively, your Nintendo Switch will be able to download games or updates while it is in sleep mode.