Is not recommended, more work is always needed once the Popcorn Removal is done since after the popcorn ceiling scraping it will be left with a lot of scrapes, loose paper, etc. and the screws and drywall joints always need more drywall compound to completely hide them.
When the popcorn texture was first done the drywallers did not spend a lot of time coating the screws and drywall joints to do the texture since the popcorn is so tick that it was not needed because the texture will cover and hide everything.
But now that a new thinner texture is wanted all the work that was not done before has to be corrected.
Priming and painting without doing all of this will result in the ceiling looking really bad, the paint will not only not hide all of this but it will make it more apparent the places where is a smooth ceiling and the scratches and joints that needed more work.
After we scrape the popcorn ceiling we always spend time fixing all the scrapes, joints, places where the drywall paper was not installed correctly, etc. and then we do the drywall texture of your choice.