I drafted Andre Johnson in the first round last year. And still finished tied for the best record in my league. You can overcome a bad first round pick. It happens with quality depth and staying on top of the waiver wire.
I think those types of scenarios depend HIGHLY on your overall league makeup: your rules, the activity and "skill" of fellow owners, etc. In your case, you may have survived AJ last year. But in other elagues, there are probably a ton of guys (I know one at least) who took Jamal Charles with his first pick and never was a factor.
I know a guy who took Chris Johnson and died a slow, miserable death. It really just depends on all that other stuff.
I think, really, the answers and opinions to this question is not so much a yes or no answer, but rather,
the answer is an indication to the level of your leagues' sophistication and evolution. When I played years ago in leagues with simplified scoring and very basic setup, drafting a guy like Marshall Faulk with the #1 overall was equivalent to punching your ticket for the playoffs and saying "See five of you guys in 13 weeks!" But in my leagues today, the difference between the guy who took Calvin Johnson at 8 and the guy who took DMAC, Charles, or even Foster just a pick or two one way or the other represents a chasm that could never be bridged.