OK, first off, I think you've got your terminology confused here a bit.
The /dev/tty* devices are not graphical terminals. The regular ones (tty1 through tty63) are mapped to virtual consoles, but are not the same thing as virtual consoles. While a desktop environment may be started on each virtual console (with separate instances), it does not actually use the /dev/tty device unless it's started manually from a shell session.
Additionally, neither virtual consoles or /dev/tty devices have anything to do with pseudo-terminals (/dev/pts/* on Linux, often referred to as 'PTYS' or 'PTS'). An application started in a non-graphical session does not use one of these unless it's started via a tool like screen or remotely via ssh. A command-line application started in a graphical terminal emulator (like GNOME Terminal, Konsole or other similar applications) is attached to one, but that pseudo-terminal is associated with the terminal emulator.
Based on what you're saying, I think what you're trying to ask is 'Can I start a graphical application on another virtual console without needing a whole separate desktop instance?'. The rest of my answer is going to assume that's what you mean (because from my perspective, that's the only thing this could mean that makes sense), if I'm wrong about this assumption, don't hesitate to let me know in the comments.
The short answer is that you probably can't achieve what you want in this way. There are all kinds of complicated things going on under the hood in a desktop environment that make everything work properly together, and that work can't be shared across virtual terminals properly without some serious effort.
You may however be interested in the concept of workspaces (called 'Virtual Desktops' in some environments, most notably Windows). They allow you to quickly switch between different sets of applications in much the same way that virtual consoles allow you to quickly switch between different command-line applications. Without knowing what desktop environment you're using, I can't give much more advice on how to use them (each desktop is a bit different in how they're handled), but they probably will cover what you want to achieve with a lot less effort.
