- Step one: Queue for something using the dungeon/raid/pvp finder tool
- Step two: Wait for queue to pop
- Step three: Use Mole Machine and teleport anywhere
- Step four: Accept the queue right after clicking a button on the mole machine to teleport
You should get the loading screen to the area you clicked to teleport to, then the loading screen for the queue pop. After loading in, nobody should be able to see you.
Spell abilities, however, will still be able to be seen.
Macros may make this easier.