When Nadal grew up, serve-and-volley was still very successful, and nevertheless he learned his own style. So I don’t think Nadal would have ever been a serve-volleyer.
Also I doubt it would be possible to win a Slam only with serve-and-volley these days anywhere, and that’s independent of surfaces. The new rackets make it impossible to go to the net without perfect approach shots. There is a reason why nobody does it today regardless of surface. Even Sampras or Becker would be helpless with their style these days. And Nadal and Djokovic were lucky that the style they were capable of was the future.
Only Federer would have success in any era, because he is the perfect allrounder.