Check your HOA documents... they control that issue. Didn't you just post about the violations?
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There is usually no statutory requirement that a board member be on a deed to property in the HOA. Eligibility is determined by the bylaws of the HOA. You will need to look at your documents.
This answer is for general purposes only, and it does not create an attorney-client relationship.
The answer is likely yes, he can run for a Board position. To confirm look to the following:
1st Check your Association's Bylaws - Do they allow non-members to hold a position or allow non-members on the Board? If the answer is yes, then he is eligible to run. If the answer is no, proceed to number two below.
2nd If the Bylaws or Declaration provide that only members may run then the Texas Property Code allows ALL owners to run for election to the Board. As a community property owner, he would be eligible to run. If the property is the sole and separate property of the wife, then he is not an owner and cannot run.
3rd Under the Texas Property Code, Chapter 209, if a Board member has committed a felony or crime of moral turpitude then that person is still eligible to run for the Board, but is not eligible to serve on the Board.
Seek legal counsel to review your association's governing documents and give you a certain determination.