You can clear TSA in T4 and walk to TBIT but remember T4 is only close to TBIT South Concourse. If you are departing from TBIT North or West Concourse, going thru T4 will still result in a long walk.

Also, as mentioned, T4 is under construction now so your results may vary - hard to predict how long the lines are at T4.

The "secret" TBIT arrival TSA is not always open but it is generally faster/shorter walk to TBIT South Concourse but not by much. The main TBIT TSA located at the back of the departure level is better if you are departing from North or West Concourse.