Ron Dayne was their 1st round pick that year. Ouch.
They also drafted Brady's teammate, Dhani Jones earlier in the 6th round (177), 22 spots before Brady went. Several Michigan players actually went before Brady.
Round (Pick) Position Player
2 (40) LB Ian Gold
4 (110) TE Aaron Shea
4 (122) DT Josh Williams
6 (177) Dhani Jones
So it's not like NFL teams didn't get a chance to watch a ton of Brady during the season. He wasn't playing at Kalamazoo U (not sure if this is a real place or not).
But even if they drafted him, I wonder if they would have kept him. People always point to Belichick getting lucky by drafting Brady in the 6th, but they overlook that he KEPT him as the 4th QB. And he kept him even after Drew came back from his injury. BB is one of the few that will let the best player play, regardless of draft position or contract.
Most teams would never have done that, and even if they kept Tom, he would have went right back to the bench after Bledsoe got healthy.
So yes, there was some luck involved. But there's also more to it than that.