I think you could only have a chance at being hired after you pass the TX bar exam, but even then, it’s a long shot.
From their website: “Generally only a person who is a licensed attorney can expect to be interviewed for a position as an assistant district attorney. In exceptional circumstances, a person who has graduated law school, taken the Texas Bar Exam and is awaiting test results may be considered for an interview.”
I hear that the office has recently lost a lot of staff with no immediate plans to hire more. It might not be a great work environment because of the current leadership or lack of staff. Maybe things will change by the time you’re looking for a job.
I knew several people with state clerkship who applied and were not even contacted for an interview — one top 10% UH, another from UT.
FWIW, I knew someone from out-of-state TTT that was a summer intern there. (He also had previous prosecution internship elsewhere, but grades were not super). So you might consider that if you want to get your foot in the door.
Although not restricted to Harris County, I also recommend checking this site
http://www.tdcaa.com/job_bank
edit: and yes to everyone suggesting the surrounding counties.