Nope, I'm afraid that won't work. Wine can't handle applications properly which use both a GUI and the console. Basically even if you got it to run, all matches would be sent to the console from which you started Wine. And if you started it without a console, the matches wouldn't show at all.
You could try to get TNM Tournament Edition to run but only the latest Build because that no longer uses a console window for the matches. In previous tests I performed, Wine chopped up the UI badly, though. So you'll have a lot of user interface elements which don't show their text properly.
I really don't recommend this - you won't have a good experience.