She'll never appear ever. The only game protagonists to appear aside from tiny cameos in movie intros are the ones on the main cast - Ash(or Red, if going by strict game canon), May, and Dawn. Dawn isn't getting kicked off the cast until gen 5 rolls around, and she'll be replaced by Gen5Girl, not by HGSS girl. Really guys, this is Pokemon. Figuring these things out based on the past 12 years of history isn't that hard.
Yes, I know I completely glazed over Kenta and Marina from the Raikou special. That's because they never did a thing outside that special, so they're roughly as important as Brendan's/Lucas' cameos in the movie intros. I guess HGSS girl could appear in her own special, but when was the last time we actually had special that weren't just two slighly important episodes aired on the same day to make up for breaks?