I don't think there is a "Round 3 qb" worth targeting in the third. Any qb that is confidently going to be available in the 3rd is not worth spending a 3rd round pick on. Look at the names people are listing (Cardale Jones, Dak Prescott, Jeff Driskell, etc.). Gabbert is a much better player and we don't need just a body to play the position.
After the top 4 qb's there's a big group of third day players that we can target with one of our multiple 6ths (Vernon Adams is probably the best bet given system fit). I guarantee you most of the names in this thread will go in the 6th to UDFA. A thread like this gets created every year and every year those "gems" are afterthoughts on draft day.
Anyone you take in the 3rd should be a starter or in the case of a quarterback atleast someone with solid potential to become a starter and everyone outside the top 4 will realistically be lucky to even be a career backup. It's a reason why there always seems to be a run on qb's in the first and then a lull until the 3rd day of the draft.
With the above said, there could be a quality qb that is available in the 3rd as drafts always end in a numbers game and an unforeseen player falling. It happens every year. Look at: Kirk Cousins, AJ McCarron, Matt Barkley, Bryce Petty in the 4th. All players were fringe first rounders at some point in the process, but fell due to a combo of numbers and concerns fleshed out during the draft process. To me, that player is Connor Cook and yes I would take him in the 3rd but anyone outside that top 4 would be a mistake taking before day 3.
[ Edited by 49oz2superbowl on Feb 14, 2016 at 8:02 AM ]