The Patriots took JG near the bottom of round 2 in 2014. The odds of him panning out are too poor to give a 1st.
A tour of teams and how their QB entered the NFL. Note that there are the "magical 11" QBs in the past 25 years that were found outside the top 5 picks between rounds 1-3. Of about the last 65-75 QBs taken in rounds 1-3 outside the top 5, only 11 panned out.
Patriots, Brady - end of the draft super sleeper
Dolphins, Tannehill - one of the magical 11
Bills, no QB
Jets, no QB
Steelers, Roethlisberger - one of the magical 11
Ravens, Flacco - one of the magical 11
Bengals, Dalton - one of the magical 11
Browns, no QB
Texans, no QB
Titans, Mariota - top 5 pick
Colts, Luck - top 5 pick
Jaguars, no QB
Chiefs, Smith - top 5 pick
Raiders, Carr - one of the magical 11
Broncos, no QB
Chargers, Rivers - top 5 pick
Cowboys, Prescott - too early to call
Giants, Manning - top 5 pick
Redskins, Cousins - one of the magical 11
Eagles, Wentz - too early to call
Packers, Rodgers - one of the magical 11
Lions, Stafford - top 5 pick
Vikings, no QB
Bears, no QB
Falcons, Ryan - top 5 pick
Buccanneers, Winston - top 5 pick
Saints, Brees - one of the magical 11
Panthers, Newton - top 5 pick
Seahawks, Russell - one of the magical 11
Cardinals, Palmer - top 5 pick
Rams, Goff - too early to call
49ers, no QB
10 QBs were top 5 picks
9 QBs are part of the magical 11
9 teams have no QB
3 are too early to call
and then we have Brady
5 active QBs in the magical 11 have Super Bowl rings.
1 active QB selected in the top 5 has a super bowl ring (Eli Manning)
The only QBs that are a member of the magical 11 that are not currently active are Dante Culpepper and Bret Favre. The 1990s was a wasteland for QBs outside the top 5.
Here are your round 1 QBs in the 1990s outside the top 5: 90 (Ware), 91 (McGwire, Marinovich), 92 (Klinger, Maddox, Brown), 94 (Dilfer), 97 (Druckenmiller), 99 (Culpepper*, McNown).
Here are the QBs taken in rounds 2-3 in the 1990s: 90 (Hodson, Peter Tom Willis, O'Donnell), 91 (Favre*, Nagle), 92 (Blundin, Sacca), 93 (Billy Joe Hobert), 95 (Todd Collins, Kordell Stewart, Stoney Case, Eric Zeier), 96 (Tony Banks, Bobby Hoying), 97 (Jake Plummer), 98 (Charlie Batch, Johnathan Quinn, Brian Griese), 99 (Shaun King, Brock Huard)
There is one franchise that is a wasteland for QBs: Cleveland. They have not had any consistent QB play since Otto Graham. They find guys who are ok for 2-3 years and then disappear & even that is rare because most are just bad. Every other franchise has had success at the position.