If someone is chasing you down and is going to be requesting the whois / registering information, they're more than likely also going to request payment details, etc. They're not too silly, I am sure they know you can input fake information when registering and get away with it. It becomes a little harder to fake the payment method information though, unless you have a fake PayPal that is being funded through funds other than your bank account (because then they can find you via your real bank account - unless your bank account is also faked)
All in all, if they really want - they can probably find you.
Maybe you should take a look into a VPS or ded***icated server to host your site, in some place like, lets say, Russia? Not sure if it will work, but it is a suggestion.