Obtaining some 4.0 functions on a 2.3 phone through rooting?
Short answer: No!

That would cause the handset to boot-loop or cause F/C (Force Close) as Ice Cream Sandwich and later, their apps are relying on the v4.x framework.

By bringing it across to Gingerbread could spell disaster and "weird" issues with the handset. 

However, bringing across Gingerbread 2.3.x apps across to Ice Cream Sandwich should work, (Paradox ahead...) as ICS upwards would have compatibility layer within their framework for running apps that target below ICS! Hope this part makes sense!