I definitely wouldn't do this; the pull down to refresh mentioned in John's answer is probably the most common gesture. Though if refreshing isn't automatic or is a common action for non-power users I'd personally recommend just sticking with a button; you have a pretty universal "refresh" icon at your disposal and refresh is quite often initiated from a button.
Additionally: shake means undo in iOS. If shake does anything it should probably be Undo (though it's pretty undiscoverable in iOS too so I wouldn't depend on people knowing that either).
I really wouldn't recommend making this particular nonstandard gesture anyway, since it's pretty easy to misenterpret physical movement of any kind as a "shake"; I've occasionally had my ipad tell me Nothing to Undo; I had to do a search to figure out why (I was "shaking" it accidentally). Shaking might even be more often discovered by mistake than intentionally, so I'd definitely warn against it if refreshing might be a "dangerous" action (e.g. it takes away something I was reading!)