Technically, but what do you need either for specifically?
If your connections to the database use direct connect, you wouldn't need application server, correct?
The command line tools administer the application server installation from what I gather.
I'm just trying to figure out whether SDE is something I need running. Previously, we had connected through SDE services, but now ALL of our connections should be through direct connect. I have a new server where I restored all of our enterprise geodatabases and am having troubles starting the services, even after syncing the users/roles. If I don't need it however, I'm going to move on to other more pressing issues 😉