That may sound like a joke, but it’s exactly what the Sixth Circuit had to consider (among other things) in U.S. v. Dedman. The answer seems to be no in Arkansas, yes in Kentucky, and no (according to Arkansas courts) as to whether there is a constitutional right to enter into such marriages — though I learned, to my surprise, that Israel v. Allen, 577 P.2d 762, 764 (Colo. 1978), had held there was such a right, even as to marriages between adopted siblings, and though the Sixth Circuit ended up not squarely confronting the constitutional question.
For more on how the case came to federal court, read the opinions. My tentative thought is that the dissent probably has the better view on the sufficiency of the evidence question. Thanks to How Appealing for the pointer.
UPDATE: I originally erroneously said that the Sixth Circuit had upheld the constitutionality of the ban on marriages between people related by adoption; I’ve revised the post above to correct that. That’s what I get for blogging from memory, even day-old memory. Thanks to commenter Doug Sundseth for correcting me on this.