No, wrong.

If a hypothetical QB simply played 2 more seasons than Drew, they would only need 250 yards per game to equal his feat, even missing the same number of games as he has.

Yes, but that means the QB would have played 19+ seasons as a starter. You have to be damn good to be a starter in this league for that long. Also, 250 yards/game is pretty good. That's 4,000 yards in a season. Even in today's game that's better than "decent". Brees's average yards per game is 284, which would be about a 4,500-yard season. That's his average, even counting his early years in San Diego where he was under 3,600 yards every season.

In a general sense, it's true that career stats like this favor longevity over skill, but only to a point. It's like goals in hockey. To get near the top of that list, you still have to be a great goal scorer. If you score 20 goals/season, you'd have to play 30 seasons to get in the top 20 of all-time. With passing yards, you're not getting anywhere near the top unless you're a first-ballot Hall-of-Famer.