Tao easily kills Goku and brings the Dragon Ball back to Red, gets paid and leaves. The army would still struggle to find the last Dragon Ball but it'd be only a matter of time before Pilaf recklessly tries to take them all, being killed by the RRA's superior technology. Red makes his wish and is killed by Black, who continues the army's campaign for world domination. Regardless how they compared to the Royal Military, Gero's expertise would allow them to gain superior technology not long after and they'd succeed in conquering most of the world. Kuririn, Yamcha and Roshi would train to stop them and after 1 year would go to find the Dragon Balls in an attempt to wish the army to be erased, though one factor would halt this plan; Tao Pai Pai. The Red Ribbon now controlling most of society and its economy would mean serving as Black's personal assassin and head of security would be the most lucrative job for Tao. On top of that, Tsuru Sennin would use his brother's position to boost popularity in the Tsuru School and essentially offer the RRA an army of highly trained students. Once Roshi learns of all this, he knows they can't be reckless and they continue to train for 2 more years. In that amount of time, however, Black would gather the Dragon Balls if he hadn't already done so and attempt to wish for immortality, only to be backstabbed by Tsuru Sennin who wouldn't want to continue to take orders from him before killing Black and wishing for eternal youth. Having had time to spar with Tao Pai Pai over these years as well as having his youth restored, I'd say Tsuru would be more or less on Tao's level at this point and Roshi would change plans when learning of this, bringing his students to Karin-to. Karin would tell them what happened to Goku and about the Choshinsui, having them all go through the training before giving each of them it. With far more serious resolve than their main timeline selves, they'd have the well honed body, mind and spirit necessary to survive it and launch their battle against the Red Ribbon/Tsuru Empire, easily defeating both Tao and Tsuru as well as convincing Tenshinhan and Chaozu to surrender. Gero manages to escape though, going into hiding. Goku is revived and continues to train with everyone before drinking the Choshinsui himself. It's doubtful Karin would view it necessary for any of them to train with Kami, so what would be the 23rd TB (though, due to the RRA likely not caring about such a tradition would likely be the 22nd here) is far more of an even competition and would see Roshi and Chaozu taking Shen and Taopaipai's places, Piccolo's spot being filled by some random fodder. Who wins here is anyone's bet, though I doubt Goku would have been able to close the power gap just from his Saiyan DNA alone and the most likely candidate for winning would be either Kuririn, Yamcha or Roshi. In any case, Goku still marries Chichi.
When Raditz shows up, things can go two ways depending on how much weaker Goku is here. In either case, I'd see him as bringing Kuririn and Roshi to help him with their survival all depending on if Gohan weakens Raditz enough for them to kill him. If not, the Saiyans conquer Earth and Freeza goes unchallenged. If so, I doubt it'd be by enough that a Kamehameha from the three would be enough, but that may further weaken Raditz enough for Roshi to sacrifice himself with a Mafuba. Despite having no knowledge of the Saiyans showing up due to Raditz never mentions it, Kami still airs on the side of caution and requests for Roshi to train with Kaio whereas the rest train with him. Goku is able to convince Chichi to take Gohan with him eventually and they train for the battle with the Saiyans. Without the Kaioken or Kaio's training though, Goku and the rest would be felled by Nappa and even a post-Kaio Roshi would end up weaker than 8k Galu due to his lack of Saiyan genetics making him take more time to adjust to Kaio's gravity and even if he masters the Kaioken and is capable of beating Nappa, he'd stand no chance against Vegeta (not unless his training has allowed him to achieve MUI
2). Vegeta kills all of the group except for Goku who he keeps to interrogate him about the Dragon Balls, but kills him once learning it'll take a year for them to be used and wipes out humanity. As there was no interaction with Piccolo, Vegeta never gets the idea to go to Namek and is forced to serve under Freeza for the rest of his life.
There was one exception to wiping out humanity though, being Gero. Assuming Vegeta doesn't destroy Earth as well, Gero continues amassing what resources he can to make artificial humans, though is obviously forced to make purely mechanical ones. He also finds the pod Goku came to Earth from based on what Roshi said on its location in case he ever needs to flee the Earth and eventually creates #19 and has himself converted into #20. They then upgrade the pod much as Dr. Brief did and go out into space to find Vegeta and get revenge on him. They eventually come into contact with the Freeza Force and wipe them out after an unknown amount of time. Gero then usurps Freeza's throne and kills Cold when he comes searching for him, setting his sites on universal conquest. Though he'd be successful for some time, it'd be inevitable that Babidi would find him eventually, have either Pui Pui, Yakon or Dabura kill #19 and mind control Gero into being his loyal scientist. Perhaps Gero's expertise would allow him to figure out how to best accumulate energy to revive Boo, but that's up in the air.
