Yes, I think this is entirely possible, with quite a small sample. 23andme.com has a quite popular gene-test that in addition to the usual things also gives you a percentage of Neanderthal heritage. What is most interesting is that 23andme scans for almost 1,000,000 SNPs, and their Neanderthal heritage estimator uses them all. This is because they base it on factor analysis (PCA), which is the same method that Aspie Quiz uses to estimate neurodiversity scores.
Anyway, a month ago I inserted a question about 23andme score into Aspie Quiz, estimating a very low (but-non-zero) answer frequency. I was lucky as Aspie Quiz was featured on US radio on Friday a week ago, and this has generated a massive amount of answers (4,000 per day since). Because of this, I now have 71 answers from people of European descent that also did 23andme, and their Aspie score correlate 0.26 to percentage of Neanderthal heritage. One-sided p is about 0.015.
I've heard people complain in the past that "I cannot relate autism with Neanderthal", but now that I have almost done this, there are other objections. I hope that somebody will eventually do a controlled study on this. All that is needed is a population of perhaps 50 diagnosed individuals with ASD and a control group about the same size. OTOH, people will probably complain that a correlation of 0.26 is too small to prove the point. What the small correlation probably proves is that neurodiversity is not primarily to be found in SNPs, and that such research will never succeed.

