There will be somebody added so that there is a third quarterback in training camp, but my guess is that is somebody who was previously signed and released by another team.
Since 2002:
6 draft picks
-- (Mallett, Robinson, O'Connell, Cassel, Kingsbury, Davey)
6 veterans with starting experience
-- (Tebow, Walter, Testaverde, Flutie, Redman, Miller)
5 veterans with NFL experience as backups
-- (Kafka, Ratliff, Rowe, O'Sullivan, Kittner)
4 players from other clubs, but with no NFL experience
-- (Teel, Hartline, Crompton, Greene)
4 undrafted free agents signing with first NFL club
-- (Hoyer, Gutierrez, Stafford, Applewhite)
2013:
Mike Kafka [vet FA] (1/24-6/10)
Thread Killer [vet FA] (6/11-8/31)
2012:
Brian Hoyer re-signed as RFA (3/23-8/31)
Mike Hartline [UDFA] (1/12-5/15)
2011:
Jonathan Crompton (1/17-8/02)
Ryan Mallett drafted in 3rd round, 74th overall
2010:
Zac Robinson drafted 7th round, 250th overall (cut 9/04)
Jonathan Crompton [rookie FA] (PS 11/2-end of year)
Brett Ratliff (PS 10/07; signed by Browns 10/11)
Mike Teel (5/21-6/11)
Jeff Rowe (1/12-5/21)
2009:
Jeff Rowe (PS 12/09-end of year)
Andrew Walter [vet FA] (8/03-9/04)
Kevin O'Connell cut (2008-8/30)
Matt Guttierez (cut 8/03)
Brian Hoyer [UDFA signed] (4/30-2012)
Matt Cassel (franchised, traded)
2008:
Kevin O'Connell drafted in 3rd round, 94th overall
Matt Guttierez (cut 8/31; PS 9/10-end of season)
2007:
David Greene (PS 9/19-11/20)
Vinny Testaverde (8/18-9/02)
Matt Gutierrez (4/30-2009)
2006:
Vinny Testaverde (11/14-end of season)
J.T. O'Sullivan (PS -10/02)
2005:
Rohan Davey cut (8/30)
Doug Flutie (4/30-end of season)
Matt Cassel drafted in 7th round, 230th overall (2005-09)
Chris Redman (1/07-6/02)
2004:
Jim Miller (9/04-end of season)
Kliff Kingsbury cut (2003-9/04)
Jim Miller (7/21-9/01)
Kurt Kittner (7/16-8/07)
2003:
Kliff Kingsbury drafted in 6th round, 201st overall (IR 8/26)
Shane Stafford (1/08-6/12)
2002:
Rohan Davey drafted in 4th round, 117th overall (cut 2005)
Major Applewhite (4/22-5/31)