Using GUI is basically making use of display server/protocol such as X.Org, Wayland.
I am thinking of using Ubuntu WITHOUT a GUI
That's the basic difference between Ubuntu Desktop and Ubuntu Server, i.e. Ubuntu Desktop have Desktop environment installed by default such as GNOME while Ubuntu server has none. If you really want Ubuntu without a GUI, you can install Ubuntu server.
I have too many unnecessary applications and packages
You can either use a minimal installation of Ubuntu which will install necessary packages only or install Ubuntu server and then a Desktop Environment such as GNOME, LXQt, Budgie, Cinnamon, Mate, etc. For installation and further reading, see What kinds of desktop environments and shells are available?
In that case will I be able to use applications such as text editors like (Atom, VsCode, Sublime text) and browser (Google chrome, Yandex, Firefox) in Ubuntu with NO GUI?
No, you won't. They require some display server to function. But you can use command line alternatives for that. For Text editors: nano, vim, pico, etc. For browser: ELinks, Lynx, etc. For their installation, see Browsing the internet from the command line.