We would really want to implement this in a new mobile HTML5 app for iphone/android devices first.
I would say offline support for mobile devices is more necessary than that on desktops.
George Orr commented
I think this would be valuable for time when users cannot access the internet. There are issues with synchronization, however. The simplicity of Checkvist is a major advantage, however, so I would not do this if it complicates the current design too much.