I already mentioned some of this pages ago. BB will kick the tires on an elite talent. He will take chances. More importantly, his job isn't on the line and BB has teflon and if this blew up and didn't work out no one would care.
But they almost certainly would offer Brown a low ball salary, a one year deal, little to no guaranteed money, and a ton of incentives. IMO, NE would want AB but AB probably won't want the Patriots . . . at least not 24 hours from his release. If AB is serious about winning then maybe he will consider such an offer. But if he is looking for big money, guaranteed money, or a long-term contract he's not getting it from the Patriots. The Patriots would structure the contract that they don't lose anything if he is an issue and cut him. And if things worked out they could be in line for a compensatory pick if he made it through the year. There is definitely a path where AB ends up on the Patriots.
That being said, only he can tell how this would impact the locker room. He usually doesn't bring someone in for way more than his long time players have been getting paid. The most recent exception was Gilmore. If BB feels like he would be ruffling a lot of feathers he probably would pass.
But make no mistake, BB would tell Rosenhaus here is their ironclad offer, take it or leave it, and he would not even listen to their side and their demands. Given that Brown is not on the Opening Day roster, his salary would not be guaranteed and they would only have to pay him week to week. They could set up a contract with very little financial risk to the team. As soon as he acted up they could release him. But like I said, there will likely be a team that offers a lot more money that would likely let Brown act like a clown and get away with it.