Does we need to use a terminal script “joplin-desktop --profile /path/to/whatever” to initiate the graphical interface?

That depends. What OS are you using? In macOS you can create an Apple Script with Automator, on Linuz you can change the .desktop file to start Joplin with an argument.

If we need, it means the terminal can not be shutdown.

I don't understand you second sentence. What does that mean? The Joplin CLI app has nothing to do with the desktop app and you can run them in parallel. But you must not use the same profile directory for both apps.
Or do you mean the terminal app provided by the OS? Why not? You can start apps in the background, and there are ways to get this done via UI elements as well.

But without information which OS you are using, nobody can give you a proper answer.