( I think the forum restricts PMs from early members. )
It sounds like this will work with Wine. MinGW most likely has been tested to generate stuff that will run under Wine. And if there are any problems they are likely known problems with easy work arounds, maybe even as easy as changing a compiler switch or something.
Hope this works for you trytykee. Linux is great, but sadly kind of at the margin. I hope this works for you, and that you can enjoy the Anyma Phi too.