Texas has somewhat unique rules on noncompetes. Here is the general rule:
To be valid under Texas law, a covenant not to compete must be “ancillary to an otherwise enforceable agreement.” Then, the restrictions must be reasonable in scope. The “otherwise enforceable agreement” requirement simply means that both parties to the contract must have made binding promises.
The usual case is when the employee signs the CNTC on day one of employment. Courts say that the employer must do more than just provide continued at-will employment for the "otherwise enforceable agreement" requirement. In this case, it's severance pay after the employment ends. I wouldn't think it would work. If I'm the employee, I take the money and fight about it later if he wants to compete--but it could be costly.
If I'm the employer, I would probably make it an incentive payment(s) either at the end of a term or paid in installments. So if the employee doesn't compete the stated time, then he/she gets the money. If he/she competes, then don't pay. That might have a better chance of being enforced by a Texas judge.