What would have happened if Goku had not trained between Namek and Frieza's arrival on Earth?

[SIAD]

What would have happened if Goku after leaving Namek, he had not learned teleportation and kept his power?

  After Mecha Freezer and King Cold arrived on Earth, what would have happened?

  There is no Future Trunks, nor Future Cell in this Timeline.

 

[Captain Cadaver]

Assuming you mean he was still at his post-Yardrat power yet without Shunkan Ido, he most likely would chase after Freeza far sooner than in the main timeline, where he only took so long because the threat wasn't imminent with instantaneous movement. He likely arrives not long after Freeza and Cold, thus killing them and causing things to go the same as in Trunks' timeline.

As for how this effects the version of the timeline Trunks travels to, everyone dies at the Cell Games when he self-destructs, unless they somehow remember the Mafuba exists.

 

[withheldforprivacy]

You mean if he had his Namek power and no IT? Freeza has killed everyone by the time he arrives, unless he toys with them first for plot reasons. When Goku is near, Freeza starts powering up to 100%, so, by the time Goku arrives, he has to face 100% Mecha Freeza and King Cold. Unless his rage for his dead friends gives him a DBS like asspulled boost, he gets killed too. Freeza's empire continues. Beerus does not wake up early, since there are no Saiyans left.