I am not truly sure but I don't think Department of Public Safety, Texas will issue non-compliant driver's license. I think you have to be in some kind of status to get temporary permit. Only 35 states in united states issue "federally non-compliant driver's license" also known as driver's licence for Undocumented/Illegal immigrants. I don't know all the states but I can name few,
California
Maryland
Delaware
Oklahoma
Virginia
Wisconsin
Arkansas
Montana

Call and ask Texas Department of Public safety tomorrow.