As a lapsed NY Jets fan, I disagree -- competent ownership and management is required more than good draft picks. To wit: Tom Brady was drafted at 199 overall, but the Jets' last two QB picks (Zach Williams and Sam Darnold) are both journeyman-level players.
I'm more of a hockey guy, which has a much stricter salary cap than the NFL, and the Edmonton Oilers are instructive here: they had a bunch of first overall picks 10 years ago (including multiple franchise players), but the team itself wasn't competitive until management changed and could build a cohesive team.