I would find it strange, and if I knew you wanted to know what it's like to nurse a baby like you explained, I would be even more put off, I just think it's very intimate and don't like the idea of feeding someone else's baby or let them feed mine.
I think you should find out how she feels first. Maybe make up a lady from this forum or somewhere, and say she nursed her friends' baby because of some difficulty, then ask your friend's opinoin, if she's okay with the idea, you can faint a spontaneous offer to nurse her baby.