The Saints would beg to differ. That's one hell of an extreme case though, especially since it does look like the league definitely locks up these elite QBs well ahead of time.
And speaking of Brees, there's another level of subjectivity of this type of look. Being the first pick of the 2nd round, he may as well have been a first rounder. In fact, he went 32nd overall in 2001 and Ramsey went 32nd overall the next year. Ramsey winds up being counted here since Houston was added to the league that year bumping up the number of teams to 32.
It's obviously subjective, but I'd be curious to see how many QBs went in the top 5 or 10 picks of the second round over that time.