These are the "actual" drives I'm talking about. I'm actually looking at every single drive in the NFL. The whole point, after all, is NOT to cherry pick specific drives from specific games, like your Saints example.
If you think most of the offensive success came when the game was out of reach, then you need to look at the season and test your theory. In 2013, Dallas ranked 6th in the NFL in total TD, and 4th in conversion percentage on any down. When the margin on the scoreboard was 8 points or less, we move up to 2nd in total TD, and 2nd in conversion percentage. IOW, the offense was better when it mattered most.
If you suspect Dallas' offense took advantage of bad teams, you can check that out too. In our 8 games against teams with defenses that ranked in the bottom half of the league in points allowed per drive, we scored 225 points on 90 drives, an average of 2.50 per drive. On average, these teams gave up 2.13 points per drive. So the Dallas offense scored 14.8% more than the rest of the NFL did against these defenses. If Dallas' offense was average, the difference should then be seen in how it performed against the better defenses it faced.
In our 8 games against teams with defenses that ranked in the top half of the league in points allowed per drive, we scored 174 points on 93 drives, an average of 1.87 points per drive. On average, these teams gave up 1.66 points per drive. So against these better defenses, Dallas scored 11.3% more than the league did. This was not an offense that beat up on the bad defenses it faced and was exposed by the good ones.