Here is a couple people I recall being mentioned, riding faired Moulton bikes-
http://jnyyz.wordpress.com/2012/09/1...ay-am-results/
This page-
http://www.bikeforums.net/showthread...peed-Challenge
says he got up to only 40 MPH, which is not really a lot. There could be different reasons for that however.
These are only partly faired with skirts however. And the fairings are open on top, which would not really be what you wanted for weather protection.
But anyway.
It has been done.