I have no experience with the demo whatsoever, but I wouldn't imagine it to be possible without doing some nasty illegal stuff to the .exe, which would be very bad.
I was lucky enough to buy it when it first came out, it's definitely worth the price of admission now even. Maybe moreso since there are so many things that have been done with the game since 2003.
I MISSED OUT on a copy of NR2003 a couple years ago.. it was sitting at a used game store and I didn't know what it was back then I just saw nascar and thought hmm $12.99 not bad.. I looked at it when it came out and it was like $60-75 here. But I never had a computer that was good enough.. so I stayed away from games like that... heck my computer is BARELY capable now