It's hard to say in my opinion. Federer is a late bloomer and a 19-22 years old Fed doesn't match up well with a 19-22 years old Nadal. And we have no proof that the competition outside of Federer back then was stronger than the players today who eliminated Nadal in the Grand slams.
One side of the coin.
Had they come up at the same time, Roger isn't the only one Rafa would be worrying about in the 2001-2003 time period. Plus, other factors also figure into the equation (racket technology and surface speed).
Suppose they were both born in 1981...
Rafa at 19 in 2001 would be facing a still-formidable Kuerten on clay (he won Monte Carlo and RG that year. Plus, he also made finals in Rome). Maybe Rafa overcomes Guga, but that isn't a lock imo. Like the 19 year-old Federer in 2001, I don't see Nadal being ready yet to win Slams elsewhere.
Rafa at 20 wins RG in 2002. Maybe he does well at Melbourne. Yes, he's better than Johansson who was hot at the time, but it's still hard to call imo. Further, I'm not sure he gets past say, Safin (who also made Finals) that year. I wouldn't favor him either if he played 2002 Lleyton Hewitt at Wimbledon (given especially the rackets and the surface speed). Somebody takes him out midway at US OPEN. Heck, maybe it's Andre, or heck, even Pete.
Federer was ready to win Wimbledon in 2003. You match the 21 year-old Nadal (which is basically the 2007 version), against Roger and I'd pick the 2003---still serve-and-volleying---version of Fed in a heartbeat. Rafa wins another French Open. Once again, somebody beats him at the US OPEN. Maybe it's Roddick, who in reality, won Flushing that year.
Federer at 23 in 2004 wins three out of four Slams. Rafa also at 23 wins a third consecutive French Open. Essentially, the 2008 version of Rafa would be playing at this hypothetical year, and I figure him being as dominant as he had been in reality on Clay. Still, he loses to Fed at Wimbledon (that five-set epic in 2008 in all likelihood would probably never have happened).
In 2005, Federer probably still loses to Safin at the Australian Open semis. But past that it gets interesting. He and Rafa would be both 24 playing at the French Open. It'd essentially be Fed vs the 2009 version of Rafa and I like Fed's chances here. By years end, at the very least Roger would still have 2 Slams. And maybe he'd still mark up an 81-4 year-end record.
In 2006, Federer once again wins three our of four slams. Rafa wins the French Open given his 2010 form.
Beyond this we can only conjecture what Nadal's form could be. He's only 24 right now. But the thing is, we've already seen Federer past 25.
I figure Federer in his mid-to-late twenties is better than Rafa would be when he gets to that age bracket. Of course, once again, this is speculation, since he's not even 25 yet. But given his style of play, it's not unreasonable to imagine his level dipping off more when he gets to his late twenties as compared to Federer.
Thus, had they been of the same age and played at the same timeline, I think Fed would still have roughly 9-10 Slams at age 25 (he won his 10th at 2007 Australian Open aged 25). Maybe even 11 given how I like his chances at RG in 2005 wherein he'd be playing against what is essentially the 2009 version of Rafa.
Just because Nadal improved earlier doesn't mean he'd be holding back and beating Federer in Slams had they come up at the same time. Federer wasn't ready to dominate during that time. But like I said, there are other guys (and conditions---racket technology and surface speed) capable of stopping Rafa from 2001-2003 even given that period's reputation for being relatively weak.
Just my 2 cents.