This is hardly a simple topic.
Does Detroit get the boosts from the city that New York or Los Angeles get? Of course not.
Does that mean FAs won't come here? Not necessarily. Aside from a situation like Chris Pronger and Edmonton, I really don't think the city a team plays in has as much of a bearing as people think it does. In any city with a professional sports franchise, somewhere within a 30 minute radius of the downtown area, there's a nice area where all the rich people live. Detroit is no exception in this regard.
Someone else brought up the Tigers and their ability to attract free agents. Prior to 2004 (at least extending back a decade or so minimum), this wan't the case. Dombrowski had to overpay significantly to attract Pudge Rodriguez, and take a huge risk on Magglio Ordonez, who was coming off of microfracture surgery at the time.
After 2006 (basically, after those two signings), the team has had more success on the market. What's the difference, then? After all, this is the same point where the Wings free agent signings started to decline. Both play in the same city, so it can't really be that. We all know the answer: the team stopped sucking. Made a World Series, traded for Cabrera, had a boatload of young talent coming right into their prime.
In summary, this becomes easy: if you win, and if your future looks bright with young talent, and you put up the money, you'll get free agents. The Wings need to prove that the next group of young talent can stop them from falling off the cliff once Datsyuk and Zetterberg retire before people will sign here without us overpaying them.
Side note: I would rather miss on every free agent ever than overpay, with some very rare exceptions. Look at how many teams are hamstrung by poorly thought out free agent contracts.