First, he won't be using any Pokemon besides Pikachu+Sinnoh natives in the gym battles. The League, yeah, he might bring some Pokes back, but Sinnoh+Pika get first dibs.
I could see possibly him asking to borrow Ambipom. Maybe. Despite it being a contest Poke, it still has the skills to battle.
To be honest, I can't see Ash doing that well in the Sinnoh League with his current team. Especially against Paul. Paul's pokemon are all stacked and incredibly powerful, while Ash's need training. So, why doesn't Ash bring back a few Pokemon for the Sinnog league? He did it in Kanto and he did it in Johto. If he would of done so, in the Hoenn league, he could of made it farther easily.
A Pokemon is as powerful or as weak as the story needs it to be. No Pokemon, including Pauls, have an established, definitive strength, nor are anybody's Pokemon unbeatable.
Hasn't even been seen in any meaningful role since Johto and battled and hasn't really ever been trained. The anime makes a big deal out of friendship and bonds and crap like that, and this Pokemon is almost a stranger to Ash.
He didn't even make a return in the Battle Frontier, probably because Corphish is too similar.
Same as above, but it at least returned in Battle Frontier for two episodes, and has a history of overcoming big odds. But even watching it battle is boring, since all of it's moves are variations of Tackle.
I also don't consider it to be very powerful, rather than getting lucky..a lot.
Has the advantage of being one of the more recognized Pokes outside of Pikachu...but is really powerful in the anime. I doubt it'll appear in the League. Wait for a Battle Zone season.
Despite it being powerful, it's moves are just like Turtwigs. Pretty boring to watch a battle.
Same as above. Strong due to being a legacy character, but there are more interesting water types to watch, though it's Hydro Pump is pretty cool., and a Rapid Spinner could help with any Stealth Rock users.
I don't know if Ash wants to risk it getting tired. Powerful, but unreliable.
In a smaller battle like a battle frontier 2v2, 3v3, 4v4, sure. But it's not much of a team player. But if some grass type had to return, I'd choose this guy.
I honestly don't even know what this is.
Way too similar to Staravia. Not very likely. If any bird was going to come back, it'd be Noctowl due to it's psychic abilities, which is really the only thing Ash doesn't have.
Muk would be interesting to absorb physical attacks and then Explode, but I doubt any main character would order their Pokemon to do that due to some censorship or anti-bonidng crap.
And to get Heracross out of the way, I love the guy and all, but he hasn't really been well trained. He's got the potential to be strong, but I don't think he's as reliable as others like Charizard.
After all, other than Pikachu if Ash challenges Paul with any unevolved pokemon, then the match isn't going to be very believable.
...The anime has never been believable, starting with a nearly untrained Pikachu taking down an entire flock of dozens of Spearows, and then beating Onix with electric attacks.