Of course you can use an airless for priming, but why stop there. An airless sprayer is the best way to paint an acoustic ceiling.
Why are you going to use a primer? Priming acoustic ceilings is only necessary if it has nasty stains, like water or nicotine stains, or if the previous paint is having problems.
A trick I learned is to use good exterior flat paint as the finish. It sticks extremely well and covers better than interior paints. For spraying a little thinning is necessary, 1/2 gallon of water per five gallons of paint. The water will help the paint soak in.
Apply in two coats using a 515 spray tip. A spray extension pole connected to your gun will make the work a lot easier. These are available in lengths from 16 inches to six feet. Spray the paint in alternating directions, one coat north to south and one coat east to west. Allow 4 hours between coats.
Check out <a href="https://www.house-painting-info.com/acoustical-ceiling.html">Painting an Acoustical Ceiling</a> for more details.