I just can't see Jane Connell as a warm, wise, and witty grandmotherly type and definitely not as a sexy, bosomy young girl on the brink of becoming a woman (mother and wife)."
When I finally saw a regional production of Mame in '94, I enjoyed it because I finally got to hear the score in its proper context. However, I did miss Norah and the transformation of a frumpy Agnes into an attractive woman, who is sexy enough to entrance the caddish O'Bannion into marrying her and consummating their union with the inevitable result.
Well, of course the combined character of Gooch in the musical is very different from Nora and somewhat different from Gooch in the play (and the non-musical movie). But to me, the combined character works fine, and I think you would probably feel the same if you hadn't grown up on the AUNTIE MAME film :-)
P.S. Given that you and I apparently agree that the whole subplot of Gooch's unwed motherhood is NOT FUNNY AT ALL, I'm surprised you keep focusing on the details of whether she becomes pregnant by O'Bannion or by some stranger we never meet.