Hard to say. But I'm fairly certain I would have found some other game series to pick up instead. Maybe I get involved with Fire Emblem, or the Tales franchise, or Atelier, or any number of other JRPG series/franchises earlier than I evetiually did? And of course, then I'd probably join a forum similar to PC except devoted to those franchises instead and met a different set of online members. I'd probably become a fan of characters from one of those franchises in the place of Leaf and Serena.
On the other hand, I think the quality of games I'd have bought would have been higher since most other franchise don't have the wildly varying quality that Pokemon does. I wouldn't have had the pleasure of playing Leaf Green, Platinum, or the Gamecube games, but on the other hand I'd have be spared the disappointment of lackluster entries lilke R/S/E, HG/SS or Sw/Sh. And I wouldn't be lamenting the current state of the franchise.
In short, I guess what I'm trying to say is that some other JRPG franchise probably would have taken the place of Pokemon's place in my life, for better or for worse.
Honestly, a more interesting question for me would be, "how would the past have to have unfolded differently for me not to get involved with Pokemon in the first place?" But most likely, if I had stumbled upon the Pokemon anime before the games, I would have been so disgusted by the former that I would have never picked up the latter. And maybe if my family had been a Sega family instead of a Nintendo one, I wouldn't have picked it up either.
