Taking everything into account, the only logical conclusion is that the Sayains devastated the earth. If Goku didn't save earth, either he would have died trying or been the culprit. If he did not defeat Nappa, then there are two Sayains. If he was the culprit, Raditz and Nappa wouldn't have died on earth, or even gone there. I have three theories as to how the Sayains did it; either Goku didn't hit his head, Goku didn't die against Raditz, or Bardock defeated Frieza. The first one is rather self-explanatory, but I will explain the last two.Goku survived the fight with Raditz
Goku survived the fight with Raditz
Some of you may think that this would have saved the earth, but this is not the case. In fact, it is quite the opposite. Had Goku not died, he would be weaker, slower, and lack the Kaio-Ken and Spirit Bomb techniques. Nappa would then have blown him away as easily as he did Piccolo.
Bardock defeated Frieza
Again, some may believe this to be a good thing. This, however, is not the case. In his final moments, Bardock did not become a hero! He merely gained compassion towards his son, Kakarot. After defeating Frieza, Bardock would have intercepted his son's ship and gone along, treating earth as a training mission. Regardless of whether or not Goku survived, the earth would be destroyed with thousands of living Sayains. If Goku was killed, we may even get to see a super sayain Bardock!
Would the Z-Fighter's earth be affected in the case of a loss?
Based on my theories, there is a slim chance either way. If Bardock is truly a Super Sayain, he would most likely have trained to the point of at LEAST ssj3, and they may have unlocked the ssg, ssgss, etc., Bardock would most definitely have the ability to destroy the earth. In my first two theories, however, it would be impossible. In my first theory, Goku would have no
A) reasons to go Super Saiyan
B) means of going ssg.
Additionally, if Goku didn't go super Sayain, Vegeta would not have had any will to do so, or the passion to achieve it. In the second theory, again, there are not enough Saiyans to achieve ssg and Vegeta would have no reason to go ssj. So only by an Goku's death, while Bardock was alive, and Bardock's rage reaching the super Saiyan level, would the earth be affected in any way.