White noise machines are recommended for people with sound sensitivities who have trouble falling asleep, including those with ADHD and autism. Whether it works well or exacerbates the issue depends on the individual, but assuming that it would simply add to the cognitive load is a stretch, and I wouldn't be surprised if in fact it worked more often than not.

One of the most popular white noise machines is the Marpac Dohm Classic, which many people (including myself) would vouch for.