It shouldn't be necessary. My last house had 'popcorn' ceilings and I hired a painter who came in a sprayed them, he used 2 coats - no primer. My brother painted his own, using a huge foam roller that he said was specifically designed for painting them, he didn't use primer either.

If you're gonna roll it on, I would suggest you primer first with a non water-based primer and a thin ply roller, then you can apply the ceiling white.

I'm not in the business, but I've found from experience that a thick ply roller and water-based paint will pull the texture clean off the ceiling, and trying to make it look right after that is a job.

I just rolled 3 coats of Zinsser Bulls-Eye Odorless (oil primer) on an old acoustic tile ceiling in a bathroom, and I am very happy with the results. They also recommend it for textured ceilings. You don't have to put anything on top of it, which is great, since ceiling paint apparently doesn't hold up well in a kitchen or bathroom.

I was also using it to prime the bathroom (which was done in oil gloss paint), so it was very convienient.

I used a split foam roller, which worked well but made a HUGE mess. Spray everywhere! The last coat I did with a 3/4" nap 100% wool roller - I wish I'd done all coats with that. With a textured ceiling, you might go with the split foam, but drape everything carefully!

Here is a link that might be useful: Zinsser Bull-Eye Odorless Oil Primer

By the way, this link might be helpful. He also mentions, as jimtnc did, that rolling latex paint over unprimed texture will pull it off (and explains why).

I also got the Zinsser Odorless recommendation from this guy's site. It can be sprayed or rolled. Also, I only had to do 3 coats in my case because the ceiling is 40 years old and stained, and I'm a total novice painter.

Here is a link that might be useful: Painting a popcorn ceiling - Natural Handyman