Assuming Kaio's statement of around 5 months being worth thousands of years of Earth training, it'd provide more benefit for their gains if there's no issues. The durability and size of the planet may be a problem though when it comes to the fighters going all out in such great numbers, so they may each have to go on group rotations of swapping between Kaios and Earth. While they're at it, I'd say the humans would develop Kaioken from training with Kaio as a means of keeping up with the Super Saiyans. Piccolo may do so too, though him already doing well in that regard from his canon training may make him not bother.
I won't go too overboard when it comes to the gains of the characters when considering Galu and Tenshinhan implied they were reaching the limits of what they could accomplish through their current training regimes without doing new ones such as the Rosat, so I'll say Goku ends up around equal in power to #18, Piccolo not massively weaker than his post-fusion weighted self and the Earthlings more or less on Base Galu's level (which with Kaioken x20 would bring them to the 100mil range in my books) and Gohan being significantly above his dad's base form. Yamcha goes KKx20 when facing Gero, offering the latter a far more significant boost than in canon. With the heart virus, Goku is brought down to around the level of his full power in canon which still convinces Vegeta he's surpassed him, though Goku is able to defeat #19 before his conditions worsens. Once Vegeta arrives, Gero shoots at the area with his eye lasers to create a veil of sand to escape and goes after Piccolo as in canon. Piccolo beats Gero as easily as in canon and things go the same until the battle with #18 and #17, where Piccolo has no qualms with interrupting Vegeta's fight with #18 and the group all fight the pair together. Though #17 and #18 still beat them, they're given somewhat of a challenge though the end result is the same. Piccolo's fusion ends up making him far stronger than in canon, though he still ends up letting Cell escape. Things progress the same until he fights #17, in which he easily destroys #17 before targeting #18. At this point, #16 either helps #18 or stays on the sidelines before defending himself against Piccolo, which will make little difference for reasons made apparent soon. Sensing Piccolo's fall in Ki, Goku uses Shunkan Ido to get him out of there before #16 can target him too. Cell takes a little longer to find #18/16 due to needing to rely on eyesight, though eventually finds her/him. Unlike #17 though, #18 wouldn't drop her guard and let Cell absorb her if still around, with #16 eventually fatiguing Cell enough to kill him. Around the time that Vegeta emerges from the Rosat, Tenshinhan decides to use the Shin Kikoho and deals significant damage to him, though not enough to destroy him. Vegeta uses this to track down #16 and finishes the job. He'd lose interest in humiliating #18 if still alive and Trunks would kill her before Kuririn can protest, bringing the arc to a quick end. Galu and Gohan still train in the Rosat, Dende still becomes Earth's Kami and things remain peaceful for 7 years.
For the Boo Arc, I'd say Gohan would have weakened down to the level of his canon self due to having no desire to fight and Galu would only be equal to Vegeta due to not having the Other World training to boost him much further. Things go relatively the same until the appearance of Dabura. In order to not get into that whole debate, I'll just say timeline changes cause him to be equal to SPC regardless of where one stands on that matter. The Saiyans become aware of how outmatched they are from his movements and go train in the Rosat, Goku and Gohan going in first and Vegeta (who wouldn't have gone in a second time due to there being no Cell Games) next. They all achieve SS2 by the end and with the gap between Goku and Vegeta being marginal, Vegeta would have no reason to want to be possessed by Babidi. As Gohan never had #16 give his speech though, he doesn't fight Dabura and instead tries to reason with him, though the increased battle frenzy SS2 provides would make him far less civil and eventually he'd fight and defeat him thanks to the training whipping him into shape. The arc ends anticlimactically.
Super remains without major change for the first few arcs as SS3 is made instantly irrelevant by SSG and Vegeta's personality in Super is more often than not a regression from his Boo Arc development. Things only start to change for the Future Trunks Arc as, without the second Rosat trip, it's doubtful Trunks would be on the level where his SS2 form could stand up to Dabura and he's killed. Black and Zamasu still go to that timeline and eventually either kill Babidi or persuade him to join them, though they wouldn't remain under the Daishinkan's radar for long and would be erased. The ToP is also altered drastically due to the lack of #17 and #18, their places instead being filled by Yamcha and then some filler participant who'd get beaten instantly. With Kaioken, the humans might be able to dodge enough attacks to stay in the game a little longer than normal, though would still be beaten fairly quickly. The lack of #17 means things are declared a tie between Universes 7 and 11 by the end and both are allowed to live, with Goku coming to the compromise with Jiren of using U7's Dragon Balls to revive Gicchin if Jiren lets him use the Super Dragon Balls to restore the erased universes.
The Broly Arc goes relatively the same other than Vegetto replacing Gogeta due to the fusion dance being unknown to the main cast and them having seen the Potara used by Kale and Caulifla. The Moro Arc also ends up without much change beyond the Earthlings being able to easily beat their fodder opponents with Kaioken before assisting against Saganbo.