Gohan kept training after Cell arc?

[Keedounan]

Here are my estimations on how the story would have changed.

* Gohan doesn't unlock SSJ3, since Goku needed to be in the afterlife, but his progress as a SSJ2 more makes up for it, making him about as strong as SSJ3 Goku (not unlike Trunks in Super). 

* Shin figures his powers won't have any effect on Gohan and telepathically convinces him to let himself get grabbed. 

* Having learned from his fight against Cell, Gohan immediately kills Dabura, which means the latter doesn't suggest Babidi to possess Vegeta. Eventually, Shin kills Babidi and the arc is over. In the end, Goku goes back to heaven, since the Earth is in good hands.

* Beerus comes to Earth and leaves due to Boo not being there to piss him off and the SSJG isn't needed. 

* Freeza doesn't learn about Goku defeating Boo (because he didn't), so he comes back to Earth unprepared. Cue Vegeta and Gohan playing Janken for which one gets dibs to one-punch him back to Hell. 

* Beerus eventually comes back to Earth after his brother provoked him in the Tournament, looking for a way to make the the Super Saiyan God appear in order to shift the tides of the fight in his favor. Shenron fills them in on how to achieve this form. The second wish is used to revive Goku to use SSJG. The third wish is attempted to locate the last Super Dragon Ball, but it doesn't work.

* The SSJG ritual doesn't work, because Vegeta lacks the character development required to become pure-hearted. The U6 universe wins the tournament due to Goku and Vegeta lacking the godly forms and Whis' training. It results in Beerus nearly killing everyone until Zeno steps in. 

* Zamasu arc doesn't happen, due to Goku either not meeting him or being too weak to be capable of defeating him. 

* U7 gets eliminated in ToP arc, resulting in Jiren winning the tournament and making his selfish wish. Zeno erases the whole universe. 

The end.

 

[Captain Cadaver]

I'd agree with most of that up to possibly the Super events. Beerus would still likely inquire about the SSG and using the Dragon Balls, Vegeta would transport Tarble to Earth. Either Vegeta or Gohan become the SSG, though either way they still lose. With Gohan still training, he'd reach God tier even if he wasn't the ritual candidate much as he did in the ToP, reaching that same level.
I believe Freeza would still train as even without hearing about Goku destroying Boo or if he knew Goku had died, it'd still be foolish to attack immediately when Goku's absence and a slight boost in power still lead to his death before. The main difference is that the time reset isn't necessary as Gohan would have enough power on his own to kill Golden Freeza. That said, Gohan also defeats Hit in the U6 tournament, though likely doesn't become good friends with Zen-Oh like his father did.
Anime-wise, the Zamasu Arc wouldn't happen indeed. Manga-wise, however, it's still highly possible due to Goku not being the main catalyst for Zamasu's change and more a means to an end. Instead, we'd probably get Gohan Black. With this being a Gohan similar in power to his ToP self, he'd already eclipse Merged Zamasu, so the threat of his power would be staggering. Gowasu would still tell the Saiyans about the Potara fusion and a SSB Vegehan manages to stalemate Merged Zamasu. Without the Zen-Oh button, however, they're eventually overwhelmed by Zamasu's broken immortality and the Zero Mortal Plan succeeds.
Back to the anime continuity, Universe 7 lose the ToP. Even with Gohan's increased power, he wouldn't gain the requirements necessary to unlock Ultra Instinct and even if bringing Goku back for it, he'd be far too weak to do anything. Jiren wins and makes his selfish wish.