Does she understand my motives?

You can't know what her motives are and it isn't helpful for us to speculate either. People join societies partly to make friends so you can't read anything into the head of one being sociable. Whatever you do, make sure you turn up to this coffee with some good questions about the society. If it become blatant that you wanted to ask her out but were too shy to do it directly that could well backfire on you. Some women might find it cute but assertiveness is certainly the more universally attractive trait. It's a nice story if this works out though, so good luck.

No baby don't listen to them, she can't wait to see you, now, get dressed and don't keep her waiting!