Yes, local controls do not get influenced by central entities.
Each subprocess is a different entity and can have unique set of controls undeneath it.
If you want to move controls between different subprocesses- You can cut,copy & paste.
In case you want to use a single control for different organizations and analyze, PC has a feature called 'Shared Service'.
With this, a single control defined under any subprocess can be used for many organizations and test it.This will further avoid user effort to create the same controls again and assign to different organizations.
For more details, you can visit the page
http://wiki.sdn.sap.com/wiki/x/XASGEQ
thanks,
Rajehswari