GT was created based on all the anime plus the movies up to movie 13 "Wrath of the Dragon". "Battle of the Gods" didn't exist yet, so the GT universe doesn't take God-Mode into account.
In universe, you have two different timelines, one where Bills never came to take Goku's measure which eventually became the GT storyline (where SSJ4 exists and SSJG doesn't) and one where Bills did come visit, Goku discovered God-Mode and we don't know what happened a decade later (if GT even happened, or if those events were preempted and if so, by how much?).
No, but that's beside the point. GT happened before Akira added BoGs. It is a continuation of everything animated up to that point, but not anything added in later. Had BoGs never been released or even conceived, GT would be exactly the same. You can't say the same for Wrath of the Dragon or Fusion Reborn because GT incorporates elements from those movies into itself. (For example, had Goku remarked on how his ultimate technique, the "Thousand Swarm of Heaven", still wasn't enough to defeat Omega Shenron, you could conclude that this "Thousand Swarm of Heaven" technique, whatever GT demonstrates it to be, must be superior to the "Dragon Fist". Because WotD came first, then GT based on WotD, among others.)
But that's not the case with BoGs. Ergo, GT does not assume the existence of SSJG and it's disingenuous to post hoc assume it did.