There are a few people locally who race CX with Woodchippers. One guy in particular has been outspoken about the advantages they offer in terms of handling. I dismissed him as a mountain biker.
To answer your question about bars and geometry, I think it's a question of reach. For a bike to fit well, the reach from the weight-bearing portion of the saddle to the primary hand position on the handlebars is the key measurement. With traditional drop bars, this is more or less effective top tube + stem length + bar reach. For mountain bikes with flat bars it's just effective top tube + stem length since the bars have no reach. Woodchippers have a nominal reach of about 80mm, which is similar to normal drop bars, but the typical hand position is on the drops, not the hoods, so they are effectively a little further back. I'd guess they fit somewhere between drop bars and flat bars. Probably with an appropriately sized stem they would work well on a CX bike.