Yes, absolutely. There is a methodology at each stage of education intended to keep as many in-state trained doctors in Texas.
Now, there's only so many residencies and fellowships to be had, so it is somewhat reduced to a numbers game. No program really avoids IMGs or out-of-state applicants (though, a couple of fellowships are always reserved for Texans -- eg. Trauma / Surgical Critical Care); it's just more competitive for non-Texans to get those available fellowship slots.
Texas opened two new medical schools within the last five years, and will open two more in the next five years; additional residencies and fellowship slots will open as well.
To make things more interesting, if I am currently a Texas resident would it be wiser to choose a university affiliated program outside of Texas with 5-6 fellowships or a small community program in tx with only 1-2 fellowships in regards to one day attaining a GI or pulmonary/cc fellowship in Texas?