If you are stopped for a DOT vehicle inspection, if you can produce an Annual Inspection that is less than 4 months old, you should be allowed to proceed immediately, unless there are obvious defects, like a blown tire or fuel leaking.
I had a delivery to make in Omaha and I needed to be there by 6pm on a Thursday evening. I could then drive about 150 miles into Iowa that night where I had four more deliveries to make the next day. They were each about 50 mile apart and I needed to be to the last one by 2pm, because that was when the forklift operator left for the weekend.
I was stopped for an inspection on the scale just outside of Omaha at about 5pm. As a result, I did not make it to the Omaha delivery by 6pm and had to stay over. I did not get to leave Omaha until almost 9am on Friday morning. Since I could not make it to the last drop by 2pm, I had to pay for a forklift operator to stay late, so I could still pick up my Friday evening load and get home to Wisconsin by Saturday.