Can an application run without appearing in the dock?

For example, Guake with no pop-up icon in the dock.

Each time I drop down the terminal with F12, it opens a dock icon. Can this be turned off so it just drops down?

An application can set the _NET_WM_STATE_SKIP_PAGER property to a window, in which case it will "skip" the taskbar, i.e. not be displayed in the taskbar. Except perhaps by scripting, or using a utility like "devilspie" that can manipulate windows as they are being created, there is no user exposed way to easily change that.

I believe that running via TTY does not add it to the dock. I cannot test at the moment, as I am not Using GNOME, but I think I used to do it this way in the past for the same reason. (If this is not the case now, let me know and I'll edit.)

That said, it seems a bit out of the way to open a tty to open an emulator.

Also, you likely wouldn't be able to access it from the current env., as opening another tty is sort of like entering another instance of the os. The way I think of it, your current env. is connected to tty1. That is why you can execute apps on these without affecting the dock, or anything else, in GNOME.

You can test it if you'd like to see if it is what you are looking for. To enter a tty terminal, press Ctrl + Alt + F[x], where x is between 2 and 12, and you will be dropped into a black screen and asked for your login credentials. Once you log in, you are free to run almost anything you like without affecting your desktop env..

EDIT

There are countless terminal emulators available via the package managers. If you need said functionality, it is a matter of finding one that doesn't associate a dock icon.

Although, if you have no icon, how do you plan to terminate hidden instances when the interface is minimized, it is still alive in memory. You would have to use top or ps with grep or sed every time to get the pid and run something like:

<pipe-outputs-pid> | kill