Since 1992, the Packers have drafted the following QBs (when drafting wasn't really a need):
1992 - Ty Detmer - 9th Round great for a 9th rounder 8-year career, 25 starts, 34 TDs 11-14 record
1993 - Mark Brunell - 5th Round Excellent pick, 17-year career, 3x Pro Bowl, 184 TDs, 78-73 record
1995 - Jay Barker - 5th Round
1996 - Kyle Wacholtz - 5th Round
1997 Ronnie McAda - 7th Round
1998 - Matt Hasselbeck - 6th Round Excellent Pick, 17-year career, 3x Pro Bowl, 212 TDs, 85-75 record
1999 Aaron Brooks - 4th Round Pretty solid 4th Rounder, 7-year career, 90 starts, 123 TDs
2002 - Craig Nall - 5th Round
2005 - Aaron Rodgers - 1st Round
2006 - Ingle Martin - 5th Round
2008 - Brian Brohm - 2nd Round (BAD PICK, complete bust)
2008 - Matt Flynn - 7th Round 7-year career, 17 TDs, 3-4 record, very good backup for GB
2012 - BJ Coleman - 7th Round
2015 - Brett Hundley - 5th Round
2020 - Jordan Love - 1st Round
2023 - Sean Clifford - 5th Round
Two First Round picks and a Second Rounder netted: AR (HoF), Brohm (bad pick), and Love (current starter with 7 starts in career)
The remaining picks were 1 Fourth and a bunch of Fifth Rounders or later. The fact that they've grabbed Brunell, Hassellbeck, Brooks, and Detmer in those picks is pretty solid drafting when they weren't drafting for need in those years.