If I have one village that spawns iron golems, could I simply move the iron golem 100+ blocks away from the village to allow more to spawn? Or will the golem have to be killed to allow more to spawn?
Yes, it's called Iron Golem Farming and it's a widely used method of obtaining an infinite source of iron golems or iron ingots.
Quoting the Minecraft Wiki:
An Iron Golem farm is an easy way to acquire many iron ingots (and less useful poppies) with minimal effort after the initial setup. It is an artificial village (or several of them, spaced far enough apart to remain separate) in which golems are spawned and then either killed immediately, or moved to a holding cell (outside the village boundary, so that new ones can spawn in their place) for later killing.