This is a short look at how a "trained Jaune" makes no difference to the story.
As the battle for Beacon waged on, Pyrrha made her decision. She had to protect her friends. She had to protect Jaune.
"Jaune, there's no time. Go! Get to Vale, and call for help."
"Huh? What are you gonna do?" Pyrrha cast her eyes to the top of the tower, where Cinder Fall would surely be. Realization dawned on his face.
"No! Pyrrha, you can't, you saw how powerful she was! I won't let you do-"
Pyrrha's fierce, deep, heavy and emotion felt hug cut him off. Her face buried itself into the crook of his neck as he slowly, returned the hug, as if begging for her to stay. She couldn't keep her voice from cracking as she spoke one last time. "I'm sorry..."
She pushed him into the nearby rocket locker, trapping him there as she used her semblance to keep him in place. She needn't have tried. Anything that can survive moving at high speeds through the air then crashing into solid concrete could survive whatever an emotional teenage huntsman-in-training could muster while in a position that restricted his arm movement.
"Pyrrha wait, stop!" Jaune begged. Tears clogged his eyes as he watched his greatest friend – and nothing more – sacrifice herself for him. "Pyrrha, please don't do this!"
Pyrrha looked into his eyes for one final time. The eyes of the boy – no, man who recognised her from a cereal box, who stuck by her when she failed to achieve her destiny, who never put her on a pedestal like others had but instead strived to be as good as her. The eyes of her best friend. And nothing more.
The rocket launcher activated, and flew to safety.
If it wasn't clear, nothing changed before season 3, with the only exception being that Pyrrha never fell in love with Jaune. You see, Jaune was never lacklustre in combat, because he never cheated his way in. He not only has no secret to be blackmailed with, he is even less likely to be bullied by Cardin (it's hard to bully the confident dude with the super tough friends, and yes, he would be confident because he has faith in his abilities). This means that there is no arc in which Pyrrha becomes more concerned for Jaune, and then becomes filled with pride after watching him prove he deserves a spot in the academy. That prevents them from deepening their relationship. It would also mean that Pyrrha is far less likely to have had those training sessions with Jaune, and even if they did they would have far less meaning to both parties involved. Which is why I decided that, instead of falling in love, they would both instead be very good best friends. Maybe even Jaune liking Pyrrha more, having more self-confidence and all that.
BONUS ROUND: What if Jaune unlocked his semblance earlier? Say, before Pyrrha pushed him into the rocket locker?
Literally nothing would change.
BONUS ROUND 2.0: What if Jaune had an ultra powerful semblance?
Now there's an interesting thought, because it has a very significant effect on Volume 3 in particular. I say this because what it changes is this; who does team JNPR select for their finals match? Pyrrha or Jaune? See, on the one hand, if they pick Pyrrha, then Pyrrha kills Penny. But on the other hand, if they pick Jaune, then JAUNE kills Penny. Cans you see the potential difference this might make?
Of course, one could argue that maybe Jaune could have changed the outcome of the fall of Beacon. Let's check that theory with this special story:
Jaune stared in worry and confusion and shock and a myriad of other emotions as he watched the machine drain something from some girl and into Pyrrha, all while Pyrrha cried out in agony. When suddenly, with a loud thunk, an arrow smashed through the other glass container, killing the inhabitant and ending the process.
Nothing changed? Probably because anyone in their right mind would turn when their best friend screams in pain, and would question the situation. Even if that does leave them distracted.
So what about the locker incident?
Pyrrha watched as the locker flew away, the mentally and emotionally confused boy inside rendered momentarily paralysed with sadness, fear and shock before realising that they were too high up to survive falling from their prison.
Nothing? Well then. I guess Jaune really was, and sort of still is, pretty much useless. Seems like that'll change with volume 6 though, now that he's discovered his healing semblance.
Plus, it'll make for cool fight scenes later on when we see someone who's been boosted by Jaune fight someone else. Can you imagine what Qrow's semblance would be getting up to?