John Wawrow of The Associated Press reports that the exemption will not extend into the regular season, instead covering the Bills' final two preseason games. Bills GM Doug Whaley apparently requested for the exemption to extend into the regular season, but that request was apparently denied.
Here's the thing, though: Wawrow also reports that the exemption does not kick in until August 27, the day that NFL teams must reduce their rosters to 75 players. (Ian Rapoport of NFL.com reported the same thing earlier Tuesday.) The Bills only have one preseason game after August 27 - two days later, at home against Detroit in their exhibition finale. As Wawrow presents it, the exemption lasts two games, but also only lasts from August 27-31 (the latter date being the cut-down day to 53 players), in which the Bills play one game. Good luck figuring that one out, because we're done trying.
What seems more certain is that Byrd won't be missing any paychecks: he appears to have strategically signed his franchise tender far enough in advance of these convoluted rules to avoid regular season exemption, and thus he'll earn every penny of his $6.916 million franchise tender.