I've never had one but it has USB ports, so it should be doing *some* local processing. Though RAM is most important with these machines. All reviews I've seen say that they run much better with 4GB of RAM.
Are the SSD's soldered to the board or can they be changed for something a bit larger, like a MX100?
Well chrome apps are mostly in the cloud which processing is done in thew cloud. I know Chrome has more offline apps but still the huge majority are online cloud apps. You can run those same apps on a windows machine inside the Chrome browser.