The Patriots offense can be so complex, the receiver almost has to have the intuition of a QB when reading the defense. The last successful player the Patriots have developed at WR is Julian Edelman, a player who converted from QB to WR just to play in the NFL. The biggest reason Edelman was successful at the position is because his father coached Edelman as hard as Bill Belichick coaches his players, so there wasn't any problems for Edelman to fit in. Edelman emerged once his opportunity arose when Wes Welker walked and Danny Amendola injured his groin in Week 1 of the 2013 season. You know the rest of this story about Edelman seizing his opportunity and getting rewarded with a 4-year deal by the team.
The Patriots have had poor luck with drafting receivers, whether it's because of injuries or inability to understand the playbook. Patriots have had to import players via free agency and trades to try to keep the offense going, but the inability to draft and develop receivers more consistently needs to change. The Patriots have tried going with fast and quick guys like Bethel Johnson, Chad Jackson, Taylor Price, Brandon Tate, and Josh Boyce and they have tried using tall receivers like Aaron Dobson to no avail. As for most of these players, injuries have either stunted or ended their careers. The only way the Patriots can develop these players is if they are able to stay on the field.
Past successes can often reveal a plan for tackling this problem. The most successful draft picks are Edelman, Deion Branch, and David Givens. The Patriots have tried to find a Deion Branch multiple times in the draft to no success, partially due to a philosophy change in the offense when Josh McDaniels replaced Charlie Weis at Offensive Coordinator. The Patriots have a David Givens comparison with Brandon LaFell, who is a few inches taller than Givens, so the idea that he will restructure/extend once that surgically-repaired foot is finally healthy. LaFell's value is maximized in New England than any other team, so the chances of that happening are very good.
So if the Patriots want to try the Julian Edelman route, the most famous QB to WR convert from the college ranks would be Ohio State's Braxton Miller. Miller weighed in at 6'1" 204 in the Senior Bowl yesterday, so he offers a bit more size than the 5'10" 200 Edelman. Braxton Miller is very good when running with the ball when he was an option QB and the Patriots offense is designed for opportunities to get YAC. That plays into Miller's strengths, but the problem for him will be learning routes. That inherent risk will keep his draft stock down and allow for the Patriots to take a shot at him on the third day of the draft.
Miller converted from QB to WR after a knee injury that ended his 2014 campaign. After the Buckeyes found his replacement in JT Barrett and Cardale Jones, with Barrett eventually taking the starting role. Miller has very good speed and is elusive in the open field, with his coach Urban Meyer expecting him to run a sub-4.4 dash. Miller was named as an honorable mention for the All Big Ten team, an honor voted on by the coaches and the media. By drafting him, the Patriots are picking up a project at WR as opposed to a more experienced player earlier in the draft. They may wind up doing that and still pick up Miller in the 4th round of the draft. If Braxton Miller is able to achieve success, the Patriots' new formula for trying to draft and develop receivers may be converting college QBs of different sizes to WR. We won't realistically know the answer for a couple years.