Probably not. The 1861 Texas Constitution is pretty explicit in stating that slaves could not be freed.

ARTICLE VIII.

SEC. 1. The Legislature shall have no power to pass laws for the emancipation of slaves.

SEC. 2. No citizen, or other person residing in this State, shall have power by deed, or will, to take effect in this State, or out of it, in any manner whatsoever, directly or indirectly, to emancipate his slave or slaves.

Interestingly, it does grant them a trial by jury for certain crimes and allows for the Legislature to demand humane treatment. It's not much but perhaps still more than what many might have expected.

Regardless it looks like any slaves born even after Houston "freed" them were still considered slaves. One example I found was Samuel Walker Houston, who was born after 1863 but was still considered to be born into slavery.(link)

Of course, they were all ultimately freed when slavery was abolished.