Not the point.
The point is that the enchantment makes a not real thing, into a real thing, when it is picked up. (does not specify how, or by whom)
So, you pick up a not-real instance (eg, dream world resident imagined version) of the not-sword using your dream avatar (since you are asleep in a REAL bed), which is likewise not "real." This action turns the sword "real", allowing it to traverse a portal to the waking world.
This requires some preparation, and some prerequisites.
1) a portal between the waking world and the not-so-real dream world, through which real objects can be exchanged. It is activated before you sleep.
2) Some reliable means of having a lucid dream to manifest in the dream world.
You then use this reliable method to fall asleep, and manifest a dream avatar. The dream avatar conjures the not-real version of the not-sword, using dream manipulation. It then picks it up, making the sword real. The dream avatar then tosses the "real" sword through the portal. Since the sword is now real, having been picked up, it traverses the portal just fine, and lands on the floor in the real world with a thud. You can then wake up, and collect the realized sword.
One could theoretically just keep conjuring them, and tossing them through for hours if they wanted.
There is of course, a catch. You cannot imagine in your hands. You HAVE to "Pick it up", which means you have to imagine it on a floor, in a cabinet, on a counter, etc--- some circumstance that requires you to pick it up first. For the mass production idea, one could imagine a machine that cranks them out and makes a pile of them on the floor of the dream world just beside the portal. Then the action of picking it up to toss it through will make it real, allowing it to traverse the portal. You just hunker down and just start picking and pitching swords through.
This could be used to amusing effect to seriously peeve off a DM if two players work together. One a dream manifesting character, and the other a plane manipulating wizard. They could conjure hundreds of pounds of metal swords, completely avoiding the normal material components of such conjuration, by exploiting this enchantment.