No. Laws aganst cohabitation, as well as those against fornication, have long since disappeared.

However, in theory, if he is married to someone else, he could run afoul of the bigamy statute:

"Sec. 25.01. (of the Texas Penal Code) BIGAMY. (a) An individual commits an offense if:(1) he is legally married and he:(A) purports to marry or does marry a person other than his spouse in this state, or any other state or foreign country, under circumstances that would, but for the actor's prior marriage, constitute a marriage; or(B) lives with a person other than his spouse in this state under the appearance of being married; or(2) he knows that a married person other than his spouse is married and he:(A) purports to marry or does marry that person in this state, or any other state or foreign country, under circumstances that would, but for the person's prior marriage, constitute a marriage; or(B) lives with that person in this state under the appearance of being married.(b) For purposes of this section, "under the appearance of being married" means holding out that the parties are married with cohabitation and an intent to be married by either party.
..."

People sometimes say that when they live in subsidized housing. But it's about who may share living quarters when the government is paying part of the rent, not about cohabitation laws.