g1smd - 11:35 am on Jan 12, 2013 (gmt 0)
You can and should always register both www and non-www in WebmasterTools.
Several of the reports are separate for each: especially the crawl and linking reports.
It's a good way of finding out who is linking to the wrong one.
There's lots of other useful things to be gleaned from looking at the reports for the non-canonical one.