Will it be possible to capture live (while recording) from an HVX200 to a computer hard drive in HD formats, and if so will the camera come with software to support this process? If it's possible but the camera doesn't come with the necessary software, what editing applications are likely to support doing this?

Oh Yeah
Plug in the Firewire and Capture to your NLE...
I hear, for example, FCP goes in smoothly with Log & Capture

Yes it's possible, and any application that supports DVCPRO-HD will allow it. That includes FCP5, Avid Express Pro HD, and Canopus Edius Broadcast. Serious Magic's also at work to make DV Rack work with DVCPRO-HD.

Windows XP Service Pack 2 supports direct connection and streaming of DVCPRO-HD data, so the basic AV/C support is there in Windows already, but a capture application needs to be written to turn that AV/C stream into a captured .AVI or .MOV or .MXF file on hard disk.