Interesting topic. I have a lot of this stuff easily accessible, so thought I'd run some numbers.
Wins are the total for the season, including playoffs. So I don't use winning percentages. To keep the numbers consistent, I used all the seasons from 1978-2013, eliminating the short seasons of 1982 and 1987. There were two fewer playoff games per season before 1990. That change consistently affects all weeks and is tiny. The differences between the league size of 28 (through 1994) and larger afterward, related to the number of playoff teams is similarly tiny. I didn't separate week 18 because there was only one year that had a week 18.
The average number of wins per team is 8.51 per season (this is far from the center of the week averages shown below because playoff weeks only contain teams with a lot of wins).
Week / Average total wins for team that won / Average total wins for team that lost
1, 9.64 - 7.05
2, 9.56 - 7.07
3, 9.74 - 6.89
4, 9.57 - 7.00
5, 9.65 - 7.10
6, 9.65 - 7.09
7, 9.58 - 6.94
8, 9.51 - 7.12
9, 9.68 - 7.08
10, 9.68 - 7.00
11, 9.67 - 7.01
12, 9.72 - 6.97
13, 9.58 - 7.08
14, 9.65 - 7.06
15, 9.50 - 7.19
16, 9.56 - 7.09
17, 9.61 - 7.13
Total, weeks 1-18, 9.62 - 7.05
So, week three stands out a tiny bit, maybe. Seems well within random fluctuation. Week one is pretty much exactly the average. And maybe a bit of a slope in weeks 15-17 as the top teams can start to prepare for the playoffs.
I don't see anything to indicate that a week one win or loss is any more important than any other week. Week one performance seems very representative of overall team quality.