Yes, but there's typically a range and the Pats are something of a unicorn here.
There are a number of franchises that hover in the top 10 regardless of their on field results... Cowboys (almost always #1), Steelers, Packers, Bears, Eagles, 49ers, etc.
And there are franchises that are perennially in the bottom 10 regardless of their on field results... Jaguars, Panthers, Bengals, Cardinals, Texans, Titans, etc.
You rarely see the kind of leap the Pats have made since 2000, largely because you rarely see a team have that kind of sustained excellence. Especially onew that was a fan base black hole prior to their dynasty. The Cavs with LeBron and the Warriors with Steph are examples of low-ranked teams that ascend to near the top. But not surprisngly, the Cavs crashed the moment that LeBron left for the Heat (and again for the Lakers). The NBA is farrrr more star driven than the NFL, but the Pats may be the odd NFL team that experiences an NBA-like dynamic in their popularity.
This is why I'm curious. Will the millions of bandwaggoners who jumped on in the past 20 years stay for this rocky ride? Some will, of course. But those who were Brady-first fans, and/or front runners, will leap off. Interesting to see how many of them there are.