No. Texas already has its own government, and it will continue to be our government until the Texas Constitution is amended.
After TEXIT, an independent Texas will absolutely have a president and a congress and supreme court, among other offices and agencies that are common to all independent, self-governing nations. Texas independence will give the power of government back to the people to vote for who they want to lead their country, as it should be. During the 9 years before Texas joined the Union, the independent Texan Nation had all of these government bodies and multiple presidents but had full control over their laws and values.