They'd probably still spend 21 hours in there, though once they came out, they'd instantly get to where Cell was via Shunkan Ido and Goku would stomp him, though likely not kill him right away. He'd probably fall down the same route as he did against Freeza and tell Cell to leave the Planet, giving Cell enough time to use a Taiyoken and start draining Gohan's energy. He wouldn't drain much before he gets stopped, though seeing the hopelessness, he decides to abandon his plan for perfection and self-destruct. Goku brings Cell to Kaio's as in the main timeline and they die, apart from obviously Cell, who gains a Zenkai and Shunkan Ido.
Meanwhile, #18 would likely come out of cover and even attempt to tell Gohan she's thankful, only to be stopped as a returned Cell wastes no time in absorbing her whilst Gohan has his guard down. Having already absorbed Gohan's energy and gained a Zenkai, this Perfect Cell would likely be on the same level as his Super Perfect self, though with Kuririn there to supply a Senzu and Gohan likely having been made incredibly angry not just at his father's death, but it being in vain, he'd likely go Super Saiyan 2. We get the fight Vegeta denied us as these two even fighters duke it out above the islands; Gohan having superior power, but Cell's array of techniques and better fighting skill making it dead even. Gohan's rage would only build up further as he eventually overpowers Cell and damages him enough he spits out #18. Gohan would then waste no time in killing him and with no explosive left within him, Cell would be forced to accept his death.
Many major plot points go similarly. Trunks and Vegeta enter the Rosat, Vegeta does again with the resolve not only to reach the level Goku was at, but to surpass Gohan and would make even greater gains than in canon due to being more aware of the wall he had to overcome. Piccolo would likely go in just to test his limits in case another threat arrived, though I doubt Trunks would go in again, likely returning to the future after going in once. The wishes to revive Cell's victims and remove #17/18's explosives go as normal and Goku doesn't get revived. There's only two major differences here; #16 is still around to be repaired, likely living at Capsule Corp and receiving upgrades so Vegeta can use him as a sparring partner when he's not bird watching and most crucial of all, there's no Goten. Whilst it's debatable when Goten was conceived, assuming it was during the 9 day waiting period to leave no Goten in this scenario makes for a more drastic change.
This changes a lot for the Boo Arc. Trunks would likely be somewhat weaker due to not having a sparring partner other than his dad, the Mighty Mask event doesn't happen and most importantly of all, there's no Gotenks. As a whole, everything goes the same until Goku goes SS3, at which point he'd make sure to try and kill Boo. I imagine he'd succeed, meaning the Boo Arc ends here, as does any major conflict in the manga. I imagine they'd choose to revive Vegeta 6 months later, though he likely would take longer to develop into who he is in Super and his "You're number one" speech would likely happen when seeing Goku fight Beerus. I'd assume Gohan wouldn't go through the Z-Sword training or become Ultimate, at least not until after the FnF Arc if taking Super into account due to needing a way to become far stronger.
For Super, however, this has the same effect as most scenarios that lead up to "What if Fat Boo was killed?" Beerus likely gets bored after a while and leaves, with Goku asking Shenron about Super Saiyan God happening later and Super proceeds as normal up until the U6 Arc, during which they'd likely have no choice but to enlist Trunks as the 5th fighter, only for him to be oneshotted by whomever he faces. The Future Trunks Arc goes as normal, other than Goku and Vegeta not learning about Potara until Gowasu tells them. For the Universal Survival Arc, however, it means that Piccolo likely takes Boo's place and oneshots Basil. Gohan having gone Ultimate far later also means he likely wouldn't have lost it's power yet, meaning he'd have more time to improve his power with Piccolo and likely end up stronger than his current self, likely a good deal above SSB Goku. This also means having Freeza be the 10th fighter happens earlier as there's no attempts to wake Boo up and nobody really has any other choice. How this affects the Tournament of Power depends on what kind of role we see Gohan play within it.