Yes:
What is interesting is that the linked article says TX does not void first cousin marriages that were solemnized out of state. The fact that TX criminalizes cohabitation is sufficient grounds for DoS to deny the visa. Issuing marriage visas, especially CR-1 visas, to people the law prohibits from living together would be illogical. They would never be able to get I-751 approved:
* if they live together, beneficiary is a criminal
* if they do not, couple is not in a bonafide marital union