To my knowledge, I don't think Mel Blanc had ever appeared on any of Lucille Ball's television shows. I could be wrong, but....!
Anyway, here's Mel and Lucy, with Kay Kyser, in a newsreel presentation of G. I. Journal from 1944. Mel utilizes his Porky Pig voice for "The Sad Sack", and, yes, that was meant to be an adaptation of George Baker's comic book military clown.
Whenever Mel had Porky sing, the stuttering was included. Country singer Mel Tillis, another famous stutterer, figured out a way to sing in a normal voice, and I'd imagine that, if asked, Jimmy Stewart did, too. Hmmmm.