I tested to see which characters’ VCs had invincibility the whole way through. I did this by using a shinkuu hadoken at point blank range in the corner and seeing if the moves won, lost, or traded. None traded, but here’s the ones that won and lost. If the move won, it means that it has invincibility through the hit, if it lost, it doesn’t.
Ryu - Win
Chun - Lose
Morrigan - Win
Alex - Lose
Batsu - Lose
Megaman - Lose
Soki - Lose
Roll - Lose
Saki - Lose
Viewtiful Joe - Lose
Frank - Lose
Zero - Win
Yatterman 2 - Lose
Joe the Condor - Lose
Tekkaman Blade - Lose
Ippatsuman - Win
Doronjo - Lose
Karas - Win
Yatterman 1 - Win
Polymar - Lose
Tekkaman - Lose
Casshern - Lose
Jun - Lose
Ken - Lose
So yeah, only six characters have full invincibility on their VCs. This is for the character who tags in, not the one who calls the VC.