Stretching, one might think the GSS suggests that to be the case. The following table shows the percentages by intelligence* who report either "often" or "sometimes" having trouble falling or staying asleep:
The "often" response for those with a wordsum score of 5 is strikingly high. It might be a transcription error or could just be noise. If we combine the bottom two intelligence groupings together, the amalgamated Dumbs becomes 56.8%, which gives us a consistent but quite modest inverse relationship between intelligence and sleeping well. Make of it what you will. It's posted mostly because I ran the numbers and so might as well make the cross-tab results available.
GSS variables used: SLPPRBLM(1-2)(3-4), WORDSUM(0-3)(4-5)(6)(7-8)(9-10), BORN(1)
* Respondents are broken up into five categories that roughly forms a normal distribution; Really Smarts (wordsum score of 9-10, comprising 13% of the population), Pretty Smarts (7-8, 26%), Normals (6, 22%), Pretty Dumbs (4-5, 27%), and Real Dumbs (0-3, 12%).