While I do not practice in TX, it is doubtful that is illegal, in part because it is difficult to define "drunk". Keep in mind that the legal limit with respect to driving does not mean drunk. However, the fact that something may not be illegal does not mean that they cannot be fired for it. Depending on the nature of your concern, it might just be a good idea to call the owner with your concerns. Good luck.
Contact the Texas Alcoholic Beverage Commission. They can tell you the rules.
Texas DWI Lawyer
My answers are intended only as general legal advice and are not intended to create an attorney-client relationship. There is no substitute for a full consultation with a local experienced criminal defense attorney. For more answers based on my 19 years of experience visit my website, www.austincriminaldefenseattorney.com
The Texas Alcoholic Beverage Commission may suspend for not more than 60 days or cancel an original or renewal permit if it is found, after notice and hearing that . . . (11) the permittee is in the habit of using alcoholic beverages to excess; Tex. Alco. Bev. Code Ann. § 11.61(11); or the permittee was intoxicated on the licensed premises; Tex. Alco. Bev. Code Ann. § 11.61(13). the word “permittee” also includes each member of a partnership or association and, with respect to a corporation, each officer and the owner or owners of a majority of the corporate stock. Tex. Alco. Bev. Code Ann. § 11.61(a)
Legal disclaimer: John Bonica is licensed to practice law only in Texas. His response is not legal advice and does not create an attorney/client relationship. The response is only intended to provide general information. The question may not include significant and important facts that would change the response. You should confer with a local attorney for competent legal advice.