It's possible, but requires a little bit of elbow grease.
You could basically check for a connection on each save or edit by using navigator.onLine.
If false, you have no connection, and set up something to store the feature in LocalStorage.
If true, push update as normal. You just need to add a notification of some sort letting user know they have data that needs to be synced when they get a connection back. Or you could do it under the hood without them knowing.
You could use that method in conjunction with this sample on storing tiles in LocalStorage and be halfway there.
https://developers.arcgis.com/en/javascript/jssamples/exp_webstorage.html
Combine that with ApplicationCache if you can and be well on your way.
I'm getting good results so far, but I have not hit the LocalStorage limit (maybe 5mb if lucky) (edit, spoke too soon. I was hitting limit, just forgot to check for it. I have a clear cache button now) and unless you are using IE9+ I don't think you can check what space is left, you'll just get an error when you run out, so I'm looking into modifying the Tile Storage slightly to add a date element or a 'viewed" count and eliminate the oldest/leaset used tiles to make room for more.
One thing I have not tried yet is using IndexedDB to store features. Maybe once I get this off the ground first.
I'm hoping to add disconnected editing tutorial into some stuff I am working on.