I've actually had a glitch where I used Magic Mirror to go back to spawn while fighting EoW and he followed me to my spawn. Don't try this though, this was probably a bug and has been patched long time ago. So, I'm 99.999% sure he will despawn if you magic mirror back to spawn.
The Eater of Worlds did not despawn before 1.0.5 if it was not in the corruption. He doesn't follow you out of it anymore.
I remember trying this quite a few times when I got started on Terraria. So far there has been only one instance where he decided to make himself at home 'Rick James' style. But yeah... If anything go for it... I'd spend ten minutes away from the house around the other direction just to be safe...