Very good question!
I recently returned from my mission in Japan.
Japanese people generally love anything different to them, especially 'white guys' so that plays a big factor in our finding. We are not really allowed approach single females (if they come to the door that is no problem) but we have to be very careful.
As has already been said, many investigators 'fall in love' with the missionaries. Not to burst your friends bubble, but I highly doubt she LOVES! this elder. She is just infactuated with him. It happens alot. You will always have people feeling things for the elders, what do you expect, they are young spiritually beautiful single guys who give you a good feeling every time you visit.
The good feeling, and the love your friend feels is the love of Christ, not the love of the missionary.
(i had to explaint this to many people on my mission)
Your friend shouldnt join the church because of a cute missionary she has feelings for, because after they transfer it will be very hard for her.
You say your friend "really wants him" she doesnt even know him, all she knows is the Elder "insert name" who he is at the moment.
Some people end up marrying people that they taught and baptised, but it doesnt always work out.
You are not allowed to write to the missionary until he has finished his mission, and you need to realise that this missionary has a life and possibly even a girlfriend back home waiting for him.
Wow I wont even get into the stories I had from my mission, but lets just say it happens alot! If there really is a problem, ask for different missionaries to teach her, so she can focus more on the gospel and not on the missionary. good luck and email me if you have any other questions :)
personal experience from my mission