Yes, it’s very possible. I was afraid of all the lag that people mentioned when they used converters or third party pcbs, so I used an S controller to modify one of my spoilt Blaze DC twin fighting stick (I have two of those) to work on the Xbox.
Followed the guidelines on http://www.geocities.com/armad1ll0/systems/Xbox_stick.htm
For most of the contacts you have to scrape like what Nasci said. I recommend doing what Armadillo did for his trigger buttons. You can easily find quite a few grounding points to solder to, but I recommend using one or two easy to solder points and daisy chaining them.
As far as I know, it’s easy to get these buttons to work:
Digital directions (D-pad)
It would be hard to get these to work:
Both analog sticks
So a 6 button setup is easy (excluding Back), but a 8 button set up will require a lot more work and understanding of analog stuff.
Inspect your pcb carefully and plan your work properly before doing anything.
To answer some of your questions, yes, you should include Back if you have a button for that. If you are using emulators, the Back button is usually used for coin.
X Y Wh
A B Bl
6 buttons are usually enough for most games, but if you want a Neogeo layout included you could possibly assign two buttons to the same output, eg:
X Y Wh A
A B Bl