This is a tough call. He certainly would have a Roland Garros title eventually, I really don't doubt that. But outside of that....I would venture to say he'd have fewer slams at this point in his career if he played back then.
In that time there would be a greater amount of threats on Grass, and I seriously doubt he would have made 3 straight Wimbledon finals back then, or win 1 for that matter. As for Hard courts...again I find it very doubtful he would have won an Austrailian by now, though nothing is impossible but like on grass, he would have a ton of threats on hard courts that could probably trouble him at the majors. While I think Rafa would have moderate success, I doubt that by this point in his career he would have as many majors as he does and hold the number 1 ranking if he player during a parallel time in Sampras's Era.
It would likely be a lot harder for Nadal to grind out victories against the likes of Agassi, Sampras, Ivanisevic on Grass, and to a lesser degree Rafter, Chang maybe even Martin, Moya on Clay. I think he would just have a variety of Rivals that would push him more than some of the current guys seem to be able to do.