No, because the selection committee actually starts the voting process the fall before the class is enshrined. Because Carter retired after the 2002 season, he was not eligible for the Class of 2007 preliminary list which was released on Oct. 27, 2006. Likewise, Bruce Smith retired after the 2003 season, and he isn't eligible until the Class of 2009.
You also mentioned that Carter was possibly left out of this year's class "because Canton only takes seven at a time." This year, they only took six ... which means that no one else, including Carter, received the minimum 80 percent vote necessary for enshrinement.
There have been only four modern-era wide receivers enshrined on the first ballot: Raymond Berry (1973), Lance Alworth (1978), Paul Warfield (1983), and Steve Largent (1995). Carter is not in their class, because numbers alone do not make a Hall of Fame career.