Barnwell found his research to be inconclusive. He determined 16.6 percent of Brady's attempts and 17.7 percent of his yardage came in garbage time (defined as up by at least 18 points any time in the second half or 14 points in the fourth quarter).
The league average for quarterbacks with a minimum 200 throws is 12.4 percent attempts and 12.2 percent yardage in garbage time. Barnwell noted other top NFL quarterbacks such as Michael Vick, Peyton Manning, Aaron Rodgers and Philip Rivers have gone below the league average numbers in these situations.
So there's a case to be made, just not a persuasive one based on that criteria.