Yes you can, but it's not going to be easy and will probably involve some programming.
What you want to do is to have konsole open in the root window (the "background") instead of creating a new window. Use the source!
If you just want to type in a command without having to navigate menus or use the mouse, (in KDE) press Alt+F2 to bring up a "run command" dialog.
If what you want to do is to start an X session with just a konsole showing, full-screen, then this can also be done (I haven't tested this). Create a file like this:
and save it as some file ending in ".sh". Change 1024x768 to match your desktop resolution. Now run:
(replacing file.sh with the name of the file)
Now, depending on your setup, you will have a file in your home directory called .Xsession or .xinitrc. Change that to:
If in doubt, use both, and make them executable with "chmod a+rx" as well. Now when you start up X, you'll get a konsole-only session you can drive from the command-line.
— Robert J. Lee