Already thought about and decided against. Either the parts were a bit warped, or I glued them together a bit wrong, but regardless the cage doesn't quite fit snugly on the swarm, and magnets wouldn't be enough to hold it together properly. And even if that wasn't the case, I'd still be concerned about paint chipping or pieces breaking from attaching and removing the pieces repeatedly.
As is, for transportation the base is magnetized to stick to the bottom of a tall plastic carry bin so that the whole thing remains upright and unhassled. It wouldn't work for shipping or air travel, but for car/train it works great. Travels in the same case as Nagash, arkhan, and other tall models. Not the most space efficient, but convenient & works well. Carry case situation also contributed to decision against trying to magnetize the cage separately, as even just the swarm itself was tall enough to have to go in the tall case anyway.