Anywhere between 0-5 seems reasonable to me.
If you want to argue the high side, they went to 5 straight ECF and I believe were Eastern Conference favorites everyone of those years, how could adding an All-NBA player at their only non-All-Star position not help them out?
On the other hand, despite some great moves to put together that title team, I have little faith in their management. Just a series of bad moves after they won it all in 2004 (and some before that too, like drafting Darko).
Summer of '04 after winning the championship, traded 6th man Corliss Williamson for Derrick Coleman who only played 5 games for Detroit before he was cut.
Lost Mehmet Okur, Ben Wallace, Rasheed Wallace, Greg Monroe for nothing.
Failed to shake things up with the Billups for Iverson trade. Instead team went backwards.
Lost the Brandon Jennings for Brandon Knight/Khris Middleton trade.
Made terrible big free agent signings with Ben Gordon, Charlie Villanueva, and Josh Smith.
Thought Greg Monroe, Andre Drummond, and Josh Smith could be the front court of the future. Considering the direction the NBA has gone since, could not have been more wrong. Like betting everything on Blockbuster over Netflix in 2010.
Just so it's not all bad, was a very good non-lottery drafter.
All that to say, what would Detroit have done with Carmelo? Traded Tayshaun Prince for Robert Swift or Sebastian Telfair or Marcus Banks? Let Rasheed Wallace walk in the summer of '04 because they have Carmelo and Prince as their forwards? Traded some other key member of the team to make Melo happy? I have serious doubts they would have made the right moves. Kind of like how we look at OKC now and think what if they kept Harden, Durant, and Westbrook, but with the Piston's demise being quicker and much worse.
Edit - or as Moranis said I was typing my response, maybe not have even traded for Sheed in the first place.
Lot of ways Detroit could have screwed up despite drafting Melo.