Only on the assumption that intelligence and stupidity are opposites. I'm inclined to think they're orthogonals.
On this view, if intelligence, in its technical quantitative sense(*), doesn't exist or (what comes to the same thing) isn't very important, then there still might be stupidity.
I'm inclined to say that daily experience suggests just this: that stupidity is a quality in itself, independent of intelligence.
No doubt we could all name people who are highly intelligent in the quantifiable sense and also as stupid as mud. My personal favorite is Richard Dawkins.
(*) There's a more colloquial, unquantifiable sense of 'intelligent' which I personally do find useful -- a more etymological sense, really, connected with ideas like understanding, insight, perceptiveness, even intuition.