I'm not sure if anyone has done this yet, or if anyone has stated whether or not the iPad's screen is color managed, but here's a test to see whether or not it is.

All you have to do is view the photo in whatever environment you want to test. This could be a photo editing program, file browser, an internet browser, or perhaps an image on your mobile phone. Some software display's thumbnails without color management, but full size images with color management. Now you can find out without guessing. All you have to do is look at the image and it tells you.

Feel free to download it. The special test profile inside the image is from Microsoft.
Don't try to edit it or convert it to a different format.