I had car issues with my last test. It was scheduled for 6pm, but I preferred not to take an evening test, so I called earlier in the day (like around 10am) and asked if they had openings if i were to come a couple hours early, and they said “sure”, so I left home in time to get there around 2-3 (I can't remember exactly). My drive is about 1 1/2 hours. So, I guess it would've been a little after noon that I left for my 6pm test. About 2 miles down the road my car was having major issues, so I turned around and called my boyfriend – who was getting ready to leave for work – and told him I needed to take his car, I could drop him off at work first or he could drive the grandparent's car or something. So, I switched cars, but he said his car would need new tires to make the trip to the testing center (we'd been meaning to get new tires, but just hadn't gotten there yet). So I drove to the place we usually get tires at, and for some reason they didn't have his size tires. So, after wasting about 20-30 minutes there waiting for service and for them to check, I drove to another place, and waited through line etc. to get the tires, then drove to the test center counting the minutes. I'd contacted the test center periodically throughout the day to let them know I wouldn't be early, and then to let them know I'd probably be late. My test center had the friendliest, kindest people of all the various test centers that I've been to for this exam and others, so I think they would've worked with me to the best of their ability, but they told me that if I was more than a 1/2 hour late the system wouldn't let the CPA exam launch. Once I got to the center, I didn't even take time to text or call my boyfriend and let him know I'd made it, cause I was right on the wire. The two staff worked together to get me processed and in ASAP, and I launched the exam at like 6:28 or 6:29. From what I gathered, it's the part when you type in your NTS/launch code that has to happen by 30 minutes past the appointment time. There were a lot of open seats at the test center and like I said, these test center employees are the most helpful, friendly ones I've dealt with, and they seemed very concerned for me as they were rushing me through the process, so I'm pretty sure that past 30 minutes late, they can't launch your exam regardless of whether they want to or not.
So, tl;dr version: If you're 30 minutes past appointment time by the time that you actually launch your test, I've been told that the test won't launch and they will have no choice but to turn you away.