1142 views | 18 | Last updated on Apr 29, 2015 Texas Trivia
On their online exhibit about the annexation of Texas, the Texas State Library and Archives Commission (TSLAC) says no:
In fact, Texas received no special terms in its admission to the Union. Once Texas had agreed to join the Union, she never had the legal option of leaving, either before or after the Civil War.
You can review the 1870 act that readmitted Texas to the United States – as TSLAC states, the act "contains no language that would allow Texas to unilaterally withdraw from the United States."