It depends on your specialty, but not for family medicine - Just like most boards,
ABFM requires an unrestricted medical license in some state to actually get board certified, so you'd be stuck in a chicken/egg scenario. You may be able to do it by getting a license in a different state, then getting board certified on the basis of that license, then getting licensed in TX.
In addition, the timeline wouldn't probably work out if you plan on working immediately after residency - people apply for their licenses *months* before they plan on starting work, and even the ABFM (which is like, the most efficient of all the certifying boards) won't certify you prior to you actually finishing residency. Even if you take the test while still in residency (which ABFM allows), you won't be certified before July - and then the earliest you could get a license to start work would be like October - being unemployed for 3-4 months would suck.
Your realistic options would be
1) Get licensed in TX without board certification - this may or may not work depending on what their policies are with regards to your specific medical school. I know jack diddly squat about the TX board, so you'd have to find out if it's possible.
2) Get a license in a different state and take your first job there for some time until you're boarded and able to get a TX license, then get a job in TX.