I would rather they react positively by opening up their iCloud API for web application for third parties. Apple already has such in place as can be seen from their cloud apps at icloud.com.

I highly doubt they would do anything to stifle Dropbox's syncing functionality in iOS. Apple is still focused on selling iOS devices and ensuring people keep buying iOS devices, they will do anything in their power to keep you happy.

Limiting Dropbox functionality on iOS would be met my swift user opposition, something that doesn't guarantee recurring sales.