Goku ate the bean/s?

[SSJ2]

When fighting Cell, Goku is given a total of 3 senzu beans to fight pre-zenkai Cell. He takes the first one when Cell initially told him to and the fight continues from there.

 

[Let's Go Fearless!]

Maybe for a 3rd time, Goku might actually beat a worned out and weakened Cell IMO.

 

[Captain Cadaver]

Since that wasn't close to Cell's full power, he could just bring out more of his reserves until Goku's stamina is completely depleted and the events with Gohan continue as normal. The difference is that, assuming Cell doesn't get a Senzu here, Cell may be too fatigued to birth the Cell Juniors, or at least weaker ones, so in the latter case, Vegeta and Trunks may be able to dispatch two.

Assuming the former happens, however, #16's words to let go may not trigger Gohan into becoming an SS2, as it'd lack the build up of watching his friends almost be killed. If Cell is very fatigued at this point, a resolved SSJ Gohan may be enough to win and due to not having the arrogance of gaining new power, he'd finish Cell off before any Self-Destructs and Zenkais occur, which also means no #18 in this scenario. If Cell's still close to his full power though, the events would continue as normal with the Cell Juniors and the rest of the arc.

Since the former is a more interesting scenario, I may cover it's ramifications for the Boo Arc and perhaps Super, given how it leaves Goku still alive.
As for #17/18, I'd assume Kuririn would wish them back to life after arguing that they weren't evil like those from Trunks' timeline and that the Saiyans and Piccolo would be strong enough to stop them at this point anyway. This would likely be what sparks #18's love for Kuririn in this timeline, with the removal of their bombs through a wish the following year being what seals the deal.

 

[withheldforprivacy]

I think the feeling we get from Cell Games saga is that, no matter what the heroes did, there was no way
they could win without Gohan going SSJ2. I think that, even if Goku had taken a senzu and the injured Cell
had to face them all at the same time, along with SSJ Gohan, who was stronger than Cell's expectations, he'd
still have won; if things came to worst, he could always spawn some Cell Jrs to help him.
Goku taking the senzu could possibly affect the future plot if Cell Games ended in a way in which Goku didn't
have to die. That meant that, in the Buu Saga, either Buu never wakes up (with Goku being alive, Vegeta
has no reason to open his mouth) or Buu fucks everybody (no SSJ3/fusions).

 

[Let's Go Fearless!]

Also, maybe Goku can reach SSjin2 first too .