No. I believe she would have to feel a genuine need before she would consider carrying a gun. Unfortunately, we all know that's usually too late.
To be honest, I don't at all encourage her to carry a gun. I feel it would have to be her idea and her choice. That way she would be more receptive to getting proper training.
She is fine with me carrying, and has no problem with my having guns and shooting. She is not uncomfortable around guns - it just doesn't interest her at the moment. I suspect she feels the same way about my guns as I do about her closet full of shoes.