Nope...They're going to select Mallett, and add him to the list of Ryan Fitzpatrick, Case Keenum, TJ Yates, and whatever new QB they're taking in the top 2-3 rounds of the draft, thus giving them FIVE backup/journeyman caliber QBs who can start a few games when needed.
When it comes time for practice, hours will be spent every day just trying to single out their depth chart, and they'll totally re-invent the game as we know it. Within the first few games of the season, all 5 QBs will see the field at the same time, thus taking away any need for other skill position players. Mallett will go on to set records as their new TE, and a high group of posters will have claimed to know his potential at the position all along, while claiming that Belichick just never got the opportunity to use his trick weapon in a live game setting.