Not necessarily. It may come to pass that Xykon and Co. teleport into the desert, search for a while, and Xykon says "Screw it, let's go check out the Gate in arctic. Killing things sounds more fun than searching." Thus, they pass within 1000 feet of the Gate without actually finding it. Granted, that was a lot more plausible before the Draketooths died and the illusions started to fail, but it's still possible.