There will be updates and they will be desirable in Linux assuming people continue creating Flash content that makes use of the new features: http://news.ycombinator.com/item?id=3621096.
Keyboard input support in full-screen mode
Improved audio support for working with low-latency audio
Ability to progressively stream textures for Stage 3D content
LZMA compression support for ByteArray
Frame label events
ActionScript workers (enables concurrent ActionScript execution on separate threads)
Support for advanced profiling
Support for more hardware-accelerated video cards (from 2005/2006) in order to expand availability of hardware accelerated content
Improved ActionScript performance when targeting Apple iOS (What the??? iOS???)
Performance index API to inform about performance capabilities of current environment
Release outside mouse event API
Refactoring and modernizing the current core Flash runtime code base
Work on the ActionScript Virtual Machine
Updates to the ActionScript language
Doesn't seem like there will be anything new that can not be currently albeit less efficiently.