I’m completely unfamiliar with the rules or types of drag racing, but if you race the person, and cross the line 1st, wouldn’t you be faster on the clock too?
Bracket racers pick a time bracket that they think their car will be competitive in. Maybe you have a fast car, so you compete in the 7 second bracket, and somebody else has a slower car, so they compete in the 14 second bracket. The other car gets to leave 7 seconds before you do, and then you have to try and beat him to the finish line.
Now, to answer your question...
Not necessarily. If you cut a "Good Light", and get off the line faster than the guy in the next lane, with everything else equal, you'd be the first to the top end lights. He could have slower reaction time, and not accelerate when the light turns green, as quick as you, but his car may be faster, so although you get to the finish line first, his elapsed time (from the time he crossed the starting line to the time he crossed the finish line, might be less. Also, in bracket racing, you select a specific bracket (E.T.) that you can not exceed. Let's say that you are in the 10 second bracket, but you actually cross the finish line in 9.90, you have "Broken out", so you lose, even if the other guy is slower. Some drivers, use computerized ignition cut outs called stutter boxes, that recognize your bracket and if you're going too fast they interrupt the ignition circuits to slow you down. In the early days of bracket racing, it wasn't unusual to see drivers actually touching the brakes to slow down, but that was deemed "Illegal", so they had to resort to other devices.
I never bracket raced. I only competed in "Heads up" racing. That's where you both leave the starting line at the same time and the winner is the guy who crosses the finish line first. We ran in classes determined by dividing the weight of the car, by the cubic inches. There were other class qualifications but that's a lot to get into here.