I believe Zack being alive doesnt magically just save the day. If by meeting SOLDIER!Cloud, it would crush him even more (because we know how he just got headache by hearing Zack's name), Zack may not shut up but it can worsen the situation he doesn't intend so he would distance himself in the end... this is just like Aerith decided to go to Forgotten Capital alone and want Cloud to take a break. This is why I imagine he may show up in final chapter of Part 2 either in Nibelheim or Temple of Ancient. But then, when Cloud wakes up, Zack and Aerith could have already gone on their own journey. They just can't see Cloud suffer and like "Okay, you get rest and lemme handle this" type of person. They are similar, even Nojima said in CC interview that he entwined Aerith's characteristics in OG to Zack as much as he could. And what would prevent Aerith to not go with Zack or vice versa? Before parting, Zack could tell Tifa all of the truth about Nibelhein incident though, but it'd be still her role to fix Cloud in Lifestream. And if Zack took black materia with him because he wanted to handle Sephiroth just as much as Aerith's with her white one, Sephiroth would likely still influence Cloud to pursue them.
Sorry, but I could only imagine the combo or teamwork of Zack and Real!Cloud, not when he was still SOLDIER!Cloud.
This is me trying not to divert the Remake plot far from Original with Zack being alive, bumping the main party, affecting the story... but everything still follows the same path because Cloud and co. (without Aerith despite she's not being dead this time) would still continue on their own. We could probably have ZackAerith's side and CloudTifa's (main party) side for us to select. Aerith won't die at Forgotten Capital and she & Zack continue to go to Northern Crater (and hey, Zack could visit Modeoheim before or after Gast's house with Aerith). But they dunno that Cloud and co. pursue them, then catch up, and imagine what would happen in Northern Crater. What if Zack & Aerith died here? Their souls could still come to appear in the final battle just like how Cloud sees them in AC to support him.
Hold on! Maybe they dont die, just almost or look like they die (red herring), and they're lost in Lifestream too with Cloud. Though, Cloud is found in Mideel and ZackAerith's whereabout is unknown, the party believe they die till they surprise everyone by come appear in final battle as Lifestream actually heals them physically. Aerith doesnt have to die to stop meteor, just lets her venture Lifestream alive and communicates with it. And Zack & Cloud defeat Sephiroth.
Then, happy ending for everyone.
But let's see!
Till proven, it's just my fanfiction.