I could be wrong but I think the major problem is the VPN wouldn't be able to continue running in the background. If I'm not mistaken, backgrounded network apps like this can only remain for about 10 minutes. Hence why if you have Ignition, it's able to stay connected for that long.
I think Hamachi would need to be supported directly by Apple, which likely wouldn't happen.
With the forthcoming ability to sync your iPhone content over a local network, a Hamachi client would let us sync from everywhere rather than just at home. An extremely valuable ability when you consider updating your podcasts (which distribution is much faster and reliable in the windows/mac iTunes client than on the phone)