With with my coreData file syncing to iCloud, can I send a link to that file or an invite to a friend (who has a different iCloud account) so we can share that info through the app?
No, you cannot do that. iCloud does not allow direct file sharing links like Dropbox. Also, you should not be directly syncing a CoreData sqlite file. CoreData has its own syncing mechanism for iCloud, and you should not sync it as a whole file. From Apple's documentation:
You cannot simply move or copy an existing database file to iCloud. Instead, you should use NSPersistentStoreCoordinator's migratePersistentStore:toURL:options:withType:error: method to migrate the database to the required location.
http://developer.apple.com/library/ios/#releasenotes/DataManagement/RN-iCloudCoreData/index.html