The only way to do it would be if someone comes out with a GPS module that plugs into the dock connector. I've seen 1 or 2 implementations of this with jailbroken iPhones, but it was mainly proof of concept and no one has any modules for sale or anything like that. Additionally, I don't believe the iPhone SDK allows access to the dock connector, so you're pretty much SOL with regards to an official supported solution.
No, there is no more of a way to receive and process the GPS signal with the original iPhone than there is a way to play a cassette tape using the iPhone.
"The product is in development and planned for release later this summer/fall available with maps for N. America and most countries in Europe. There will be several enhancements that will make the solution more attractive to even the 3G iPhone's GPS applications which we will be announcing soon. We still do not have an exact release date or pricing set as of yet but I will email you again with future updates. You may also want to check out the FAQ on gomite.com for more information."
That one should work for almost any good browsered phone, since you're just accessing the GPS unit's onboard web server over WiFi. Slick idea.
Of course, it's no good for other apps, since they have no idea how to access it. You can only use whatever apps they put in the device.
(They could do something clever like letting you set bookmarks on it, so you could search from a webpage on their unit, with the location embedded, out to Google or whatever.)