No, a tame GCS is not a requirement. In fact, the silk farm described on the wiki relies on it NOT being tame.
Using a wild GCS has the side effect of blocking migration in the cavern it came from, as that cavern suddenly gets a roaming member when you remove the GCS from its cage and locks it into a room.
My preferred silk farm uses undead as bait, which means the GCS can be either wild or tame, as both are hostile to undeads. In that construction, two rooms on the main level is provided for the GCS and the bait respectively. The bait one I brick closed, while the GCS one uses a stone door (a GCS is a building destroyer, but it's too close to the door to be able to destroy it, so a wooden door should work as well). These rooms have floor hatches activated by levers to allow you to disable the farm. On the level above the main one two locked hatches are placed above the rooms and the bait is pitted into the front one, while the GCS is pitted into the back one if it's hostile (if it's tamed you can just lead it to a pasture in the back room on the main level, but make sure that's done before the undead is pitted, or the undead will scare the animal herder).
On the level below the main level you have a cage trap under each hatch so the bait and GCS are recaged when dropped (again, a tame GCS can just be led away, but the undead blocking retraining means there is a significant risk the GCS goes wild). One important thing is to remember to remove the GCS from the pen/pasture before dropping it onto a cage (or leading it to one) or your dorfs will try to lead the hostile GCS back to the pasture/haul the tame GCS back and forth between the cage and the pasture indefinitely.
If you're using a wild GCS exclusively I guess you can just as well use the wiki version with dorf bait (cats and dogs are not attacked by a wild GCS, probably because they're not considered hostile to it. I don't know what animal bait would work. War trained dogs?).
Note that pitting isn't failsafe. At times the pittee will break lose and a battle breaks out, so you can lose both the GCS and the bait that way.