Using Saichoro as a benchmark, it can be assumed Namekians seldom live past 500, so the effects of the Rosat would cause Daimao and Kami to die within 2 years of this happening. Obviously, this means the Dragon Balls are completely removed from the story, so Goku never encounters Bulma and continues living by himself. The Red Ribbon Army still try and take over the world, so unless Tsuru Sennin was never swayed towards a more evil path by Mutaito being overpowered by Piccolo as implied in the anime, the RRA secures world conquest. With no threats worth building up defences for though, Gero never creates anything stronger than a battle jacket and Raditz has no problem destroying any opposition. The main question would be how Goku would react to him when this is a Goku who's only had Gohan as a guide for a short part of his life and his early self displayed some level of Saiyan mercilessness. Thus, the plot goes in one of two ways:
1. Goku refuses and is killed. Raditz takes over Earth and the Saiyans never rebel against Freeza.
2. Goku accepts and Raditz takes him on missions to train. They spend many years under Freeza's command before the Zenkais they gain convince them to plan on overthrowing Freeza. Without something similar to the events on Namek or regular access to healing chambers though, it'd either remain a pipedream or the Saiyans would be killed when not knowing of Freeza's greater transformations, with Freeza's rule over the universe remaining constant unless another factor like Dabura or Beerus decides to change that.