According to that iOS developer link it appears that iOS is capable of color management activities but in practice it sure looks like no one cared enough about it to implement it. That Apple made color management opaque on iOS is a thought made quite clear.
I suppose if we had the time, we could effectively color manage our images "upstream." Here's what I propose:
1. With whatever profiling software you may be using, get the color numbers for the swatches it uses to create the profile.
2. Create images using those profiles, or make a tiny web site that can cycle through those colors.
3. With a color reading device connected to your computer, read the colors on the iOS device.
4. Create a device profile.
5. Convert your images to your iOS profile and put them on your iOS device.
6. Profit.
This could work if you want to use your expensive software and equipment you already have, though it might be easier if you just use the Spyder app. I can't tell if Spyder wants you to open images using its own iOS app (wherein the profile only works in the Spyder app) or if the profile created affects the entire system.
Enjoy,
Bruce Jamieson