Nah. Tom Brady is one of the best QBs of all time. Joe Montana was in a "system" too in the 80s with the 49ers. The west coast system fit his talent and abilities very well. But he made the most of it by executing the plays very well in the big moments. Just like in the Super Bowl 20-16 win over the Bengals. He made all if the right decisions and throws leading the niners down the field 92 yards for the win. Did it help having Jerry Rice at WR? Absolutely. Did the system fit Joe Montana well? Absolutely. But, as we have seen other QBs try to run the west coast system with no where near the precision of Joe Montana.
Tom Brady does operate in a very good system. But look back at his passing numbers his first and second years. The Patriots were a run first team at that time. They actually stayed that way for their first 3 Super Bowl wins. In the 04-05 season Corey Dillon rushed for 1654 yards that year. The Patriots became more of a throw first team after those Super Bowl wins. That was due to how Tom had progressed becoming a even better thrower and passer. He started out has a a very good passer of the football but not the best thrower. He made very good split second decisions passing the ball. But the balls didn't have the zip in them at that time. After several seasons though Tom became a better thrower of the football. His throwing mechanics and foot work got better with each season from 2001-02 through say 2006-07. He got to where he could throw the football on a rope 35-40 yards and be very accurate with it has well. This is why he had that monstrous year in 2007-08. He had Randy Moss of course which made it easier to throw the ball down field. But also by this time he had the throwing ability to really wing the pig down the field as well. Go back and watch Tom's throws in his first season and then watch his throws in the 2007-08 season. There's a BIG difference in the velocity in his deep out throws and his down the field throws as compared to his first season starting.
All QBs who are hall of famers have played in the right systems for them. Whether it be Johnny Unitas, Joe Montana, Dan Fouts, Dan Marino, or Bart Starr. Truth be told Bart Starr is the most underrated QB in the Super Bowl era. He won 5 championships with the Green Bay Packers. Everyone says he was surrounded by a high number of Hall of famers. Which is true. But look at Bart Starr's numbers in the post season. 9 wins and only 1 loss in the post season. 15 TDs to only 3 ints. In an era where QBs weren't winging the pig all over the field and the throws weren't dip and dunk throws usually either, his numbers are very impressive. Plus the Green Bay Packers were a run first team with Jim Taylor and Paul Horning running the ball quite often. So when Bart Starr was called upon to throw the ball it was imperative that he make the right decision and a good throw. Which he obviously did given his outstanding passing numbers.