No. As of August 2013, the Green Bay Packers have not had a starting quarterback that has been African American.
Currently no NFL starting quarterbacks are former Green Bay Packers
Aron Rodgers and Matt Flynn
The Green Bay Packers have had numerous quarterbacks in their long history. Their most famous and recognizable are Bart Starr, Brett Favre, and their current quarterback Aaron Rodgers.
Akili Smith. No one else
Bart Starr was the quarterback in 1970. This was his last year as quarterback for the Green Bay Packers.
As of the 2010-2011 season, the Green Bay Packers have three quarterbacks. Their starting QB is Aaron Rodgers. Their second string QB is Matt Flynn. Their third string QB is Graham Harrell.