Well if it's an asp.net application, then I don't see why it wouldn't, since the app is really only delivering html to the browser.
If it's a winforms app, then no, it won't work because there is no .net framework download for mac. Although there are several projects under way to move .net to other platforms, that's not being done by MS, of course, so it's hard to say whether any of those will work or not.