Walls and Ceilings - Popcorn Ceiling

I had to replace a sheet of drywall in a popcorn ceiling due to water damage. What are the chances of spraying the new drywall with popcorn so that it matches the rest of the ceiling and doesn't look like a patch job?

Depends on several factors. First the new rock needs to be hung and finished so it lines up well with the rest of the ceiling. Then you need to have the same size popcorn - fine, medium & coarse. Then with a little skill the popcorn can be sprayed and blended in. You may need to paint the ceiling to completely hide the repair - difference between old and new popcorn color.

marksr is right on
There is another option to paint: Do the patch then spray it with aggegate as close as possible. Let that dry and take a look at it. If it matches you are done. Look at both color and texture match. Then if it doesn't match spray new popcorn on the whole lid. I think that's easier than paint. Now to warn you I've heard stories about people spraying popcorn and the moisture in the new loosening the old and all of it coming down. I've sprayed several acres this way and it always has worked. Get the new work dry as fast as you can. This time of year open some windows, run some fans. Drink a pop and when it looks like it's going to stay then clean up and move out.