A few things.
I.
Keep in mind that this fic is more based on the game but still includes anime characters.
But you have Dawn as a cast member, which is rather awkward, considering the anime has a counterpart traveling with Ash. In other words, the problem with crossing casts is that if you have a character whose name is the same as a game counterpart (like Dawn), the audience will think you're defying canon by taking one of Ash's canonical companions and giving her to Sapphire.
One way to avoid this confusion is by using one main cast or the other but not both at once. So, for example, instead of using Ash, try using Red. This also means that you'll have to base the starter selection process on the way the games worked (with Red and Blue choosing starters and leaving one behind -- perhaps for Sapphire), but it's only a minor change compared to having to explain that the Dawn traveling with Sapphire and the Dawn traveling with Ash aren't the same person.
II.
Sapphire appeared to have dropped completely off the map and was never noticed widely by the public. She worked for Prof. Oak instead of going off and becoming a trainer.
....
because over time she had became quite popular in the Johto region and the Hoenne region. When she returned to Pallet Town she was praised for being the greatest trainer the town knew. This was due to her massive sucsess in the Pokémon League.
Wait, so if she was never noticed by the public, how exactly did she become popular in Johto and Hoenn? Also, how exactly did she manage to be so obscure while being a huge success in various leagues? Not to mention didn't you just sort of contradict yourself in saying that she wasn't a trainer... but then that she totally was? O_o
III. I'm mostly concerned about the fact that Sapphire sounds a bit Sueish. Basically, this is a list of her traits that you've given us:
1. She's an exceptionally good trainer, even going as far as to become a League Champion.
2. She apparently has a fan following (or is otherwise incredibly popular) in two different regions... despite having dropped off the radar during that time.
3. Two canon characters beg to be her companions and go out of their way to be matchmakers for her, even if it's not entirely within their characterization. (Aren't Rowan's assistants usually focused on studying Pokémon or filling up the 'dex for their mentor -- which would be Rowan? Granted, it depends on
which Dawn you're talking about here, but assuming this Dawn is game!Dawn and not anime!Dawn, she'd probably be more focused in the drive to get more Pokémon for the sake of research/filling the 'dex.)
4. She's old friends with another canon character and is, in fact, in love with him.
5. ...And she ends up with him.
6. ...And he's a fairly popular canon character.
7. Not one but
two evil teams unite (even though they technically have different goals, with Rocket being an organization just out for world domination and building the ultimate crime empire whereas Galactic is looking to destroy the universe and remake it in what their leader envisions to be the perfect world), only to go head-to-head with the character, who, as the summary implies, will single-handedly defeat them.
In other words, you've got a powerful character from the get-go who has tons of skills to defeat the enemy, fans, and a soon-to-be boyfriend while other characters seem to exist to support her (e.g., Dawn and Lucas serving as matchmakers) but aren't entirely true-to-canon. While Sapphire herself is a canon character, it just feels a bit like this may just end up being a bit over-the-top. I would suggest playing with her character a bit more. Maybe tone her down a bit and come up with better explanations as to why Rowan chose her (other than she's immensely popular and skilled, so he heard about her from her reputation and not just from Oak's good word), why he needs her to talk to Dawn and Lucas (considering at least one of them was his personal assistants already), and how she and Riley are getting together (without taking Dawn and Lucas OOC).
Also, do a bit more research into canon. Really look at, for example, Teams Galactic and Rocket. While they're both evil syndicates, they're not after the same goals. For that reason, they're not entirely compatible with each other. Likewise, because you're using canon characters, you've really got to get to know them. Talk to them again in the games and maybe replay parts of the games if you can in order to figure out how they'd actually act.
Finally, remember that it's perfectly okay to have a character who isn't godly-powerful. A diligent research assistant is just as or even more interesting to read about than someone who's already a champion who swept through the Elite Four. I say "even more interesting" because it means that when it comes time for the final battle, your reader won't know whether or not that research assistant will be able to defeat the bad guys -- or, at least, how that research assistant will do so. The ordinary character will need to rely on a more creative scheme in order to save the day, whereas the champion will probably rely on straightforward force and is destined to win anyway.
Other than that, it sounds like a pretty straightforward OT story in which a character travels through Sinnoh to collect badges and work with two other characters who aren't necessarily trainers as well to defeat Team (insert something here), combined with a standard shipping story. To be frank, without the possible Sue, it actually sounds rather generic. I mean, what plot description we get sounds pretty much like a lot of other OT stories out there (while the matchmaking stuff smacks of romance stories in certain ships), but you spend a lot of this post building up your character but not much actually describing the plot itself. While I don't expect you to reveal important details, it'd be nice to get something else -- like, for example, a vague idea of what the evil teams are doing, why Rowan chose Sapphire, and basically all those other things you seem to start mentioning but seem to wander away from for the sake of describing something completely different. It'd also be cool if there was more of a focus on Sapphire's task to fill the 'dex, considering that's why she was called to Sinnoh in the first place, but mostly, my point is we don't really have much to comment on because you focus so much on describing the character and what's going on with the character instead of the events surrounding the character. Yes, this is all just a summary/"do you like this idea" post, but even then, it feels like you're falling short of actually presenting a coherent set of ideas -- even going so far as to shrug them off completely (in the case of Sapphire's task from Rowan, for example).
In other words, I'd hate to say this, but this all sounds incredibly disjointed. O_o It's contradictory in places, and it seems to be all over the place in terms of plot, probably because so much time is spent focusing on Sapphire. Work on it a bit more and read over your ideas to straighten things out, I should say.
Also, you may want to get a beta. (There's a sticky for them in Writer's Lounge.) It's just that there's a lot of spelling oddities that I can spot just in your summary, some of which can't be caught by a spell checker. I don't know if you proofread, but it's good to be on the safe side.