Is it possible to get the gnome-terminal in GNOME 3 to be borderless, similar to how urxvt looks? Without the big top of it that says Terminal with your working directory or the menu bar?
You can disable the menu bar for gnome-terminal in its application menu (in Gnome 3 this is a drop down in the top bar). You can also edit your default profile to not include scroll bars, the menu bar, etc in net terminals.
Beyond that, the window chrome (the border, title bar, etc) are decided on and drawn by your window manager (in Gnome 3 this is Mutter). I don't think there is an easy way to make Mutter not draw borders on some windows, but you can check the Gnome extension library for something that does that.
Enabling compiz, will give a large selection of effects like borderless windows. I am using Terminal without window border also, I don't use compiz, but when I open my terminal window, I click on F11 to make it full screen.
If you want to hide the menu bar also, click on : "View" -> disable "Show menubar".