See this thread (before the shit slinging started about whether different frame materials can allow flex AND harshness, etc.) for opinions on TT'ing
http://www.singletrackworld.com/forum/topic/road-bikes-getting-confused
Sure you can TT a CX bike – you can TT a shopper if you want. You are unlikely to win (although I suspect Bradley on a shopper might stand a chance in the club 10) but the point of TT's for most is to beat your own PB, and therefore instead of souping up what isn't designed to be souped up – why not just ride what you have.
In that respect, a CX bike is a reasonably good all rounder, heavier than a road bike and more akin to a sportive geometry but still perfectly rideable. I have 2 sets of wheels for mine mainly to avoid the faff of changing tyres depending on the ride I'm about to do.