Sharing my knowledge thoughts on the matter - CrossWalk (CW) is just a runtime which helps get full potential of HTML5, because it supports more and advanced HTML5 features than Android's default WebView, and it helps to have a consistent UI in all Android apps, irrespective of who is handset manufacturer.
For that, app will contact or work through CW API and it will interact with Chrome runtime to ensure that there is consistency and what ever gaps are present is filled by CW.
As we can see in below architecture diagram, it still talks with Chrome runtime, so it wouldn't change any runtime rules apart from UI based rule or APIs etc., and at-least it would not change any storage rule or underlying mechanism.
There are issues related to local storage access with CW, but those issues are related to API, so as per me you can expect same storage mechanism, limits and rules with CW.
Hope this helps!
