No, Romney wouldn't pick Brown as his running mate, because both are Massachusetts residents, so if the ticket carried their home state the Massachusetts electors would not be able to vote for both of them in the electoral college. (That's why Cheney had to re-establish his Wyoming residency in 2000 to run with Bush--otherwise the Texas electors couldn't have voted for both Bush and Cheney.)
Of course it's a moot point--Massachusetts is unlikely to vote Republican no matter who is on the ticket, and Romney isn't going to be the Republican nominee.