When Vegeta was fighting the Z warriors on Earth he came to near death. Vegeta had the upper hand for most of the fight but towards the end Vegeta was put through a lot of pain (Genki-Dama, Oozaru falling on him). After all of this though, Vegeta was still willing to fight until he was finally defeated. Kuririn had Yajirobe's sword and was about to kill Vegeta until Gokou stopped him and let Vegeta retreat because Goku thought Vegeta could change his ways. What if Kuririn hadn't listened to Gokou or Gokou was unconscious and couldn't tell Kuririn to stop. Vegeta would have then been dead.

Gokou, Kuririn and everyone would have still healed at the same time and been off to Namek. Most of the events would have been the same except more Nameks would have been left alive because Vegeta killed a large portion of them. The Dragon Balls that Vegeta had collected would probably result in Freeza obtaining them. Gohan obtained his one Dragon Ball from Vegeta and with Vegeta out of the picture, Freeza would have all seven Dragon Balls.

The Dragon Balls would be fairly useless to Freeza because he would not know the password to use them. Namek Elder might also have been killed by Freeza which wouldhave gotten rid of the Balls, but Freeza was probably smarter than that. Dodoria and Zarbon would probably also be alive. If they had some how provoked Gohan and Kuririn. They might have beaten him, but it is irrelevant.

Kuririn and Gohan also kept a fairly low profile so the Ginyu Force would need not be called especially now that Freeza has all the Dragon Balls. Freeza would probably be killing off random Namek's until he got the password. Gohan and Kuririn would probably try to stop the killing which could easily result in Zarbon killing them both.

When Gokou reached Namek he would probably kill Dodoria and Zarbon if he had to and try to fight Freeza. Without Gokou being beaten by Ginyu, he would be much weaker and would not stand a chance against Freeza. Gokou also probably would have not gone Super Saiya-jin. Regardless, Gokou, Kuririn and Gohan would most likely all be killed by Freeza. After this Freeza would either receive the password or not, either way, he would still carry out his intentions one way or another.

So, in some way leaving Vegeta alive actually saved the Earth. Even in the original storyline Vegeta saved Gohan and Kuririn on Namek and as the series progresses, Vegeta saves more and more people (he also kills more though). Also, Dragon Ball Z without Vegeta in it would be much more dull because Vegeta was a really cool character. Once again, this is just my interpretation of what would happen. The events are unknown and probably several different versions could be created.