Can iCloud be used to export relatively large amount of data for a user to easily access?
If you upload anything to iCloud it will be available to all devices logged into that iCloud account provided there is a way to access the account directly. If I upload a picture to iCloud using my iPhone I can later drag it to my desktop on my Mac. In OS X (I believe in Yosemite and later) there is the "iCloud Drive" folder in the sidebar, (which may or may not be on) which you can use to access this directly. To turn this on


Go to Finder -> Preferences. (Or press ⌘+,)
Go to the Sidebar tab.
Check iCloud Drive.


Of course you'll also need to be signed into iCloud Drive and have it turned on which is possible in System Preferences -> iCloud.

iOS 9 also includes an "iCloud Drive" app which gives pretty much the same view. The only difference is non-Mac devices may not be able to open files that you put up there, but since you're uploading images that's fine as long as they're in a supported format.

On a non-Apple device there's always iCloud.com.

Things in iCloud will stay in iCloud until the user deletes them. Or unless iCloud servers get blown up. Whichever comes first.

However if these images are to be published in some way other than for personal use you should probably use FTP and allow the user to upload them elsewhere. Though this would be for something along the lines of a web design app.