No, I don't think it can unfortunately (though it would be nice).
The logic to prevent multiple instances takes place in a completely separate part of the program. I would be able to display the running instance, but not handle the folder name.
I could allow the "prevent multiple instances" code to be disabled by a registry key. That way, only people who wanted to accept the risks would be able to use it (the risks being that stored settings and Favourites could get messed up).
Let me double check though....