There is invincibility after spawning. I'll prove it in the Advanced Technique thread later. You can see it on IGN's video of MetaKnight's Ship.
There was never invincibility in Sudden Death. There is no respawn in Sudden Death. you die... Game Set
As for invincibility in Edge Recovery, there is, but I don't remember the video. I think MetaKnight or Mario does it in GameVideo's (1up) Diddy Kong Final Smash video
Edit: Okay, I take that back. Respawn Invincibility is gone but grabbing EdgeGrab Invincibility isn't. Look at ssbros_shipbattle2_101207_wmvhd.wmv on IGN MetaKnight is invincible on an edge as an item passes him.