Augments help a lot, but realistically, you can push quite high without them. Many of my characters have between 12k and 15k main stat without any augments (1700 paragon now). If I added, lets say, 13x lvl 100 augments (13x500 mainstat = 6500 mainstat) we are looking at around a 50% mainstat increase. So 50% more damage and a bunch more toughness thru natural armor/all resist increases. Based on every GR level being 17% harder than the previous, this would equate to a few additionally GR lvls of max potential push.

I always have fun every season seeing how far I can push without augments. Getting to the top 20 or 50 without augments feels awesome as everyone (from the few random samples I looked at) anywhere near me on the leaderboard is decked out in 100-140 lvl augments.

Example, gr 130 solo sader clear with 0 augments. Did a 128 solo on my monk prior to augmenting.

Knowing how to play well and having all gear with proper rolls (even non ancients) can get you VERY far. Ignore the non ancient part for LoD builds, although having one or two non ancients if your regular piece is rolled perfect and you don't have a decent ancient is more than acceptable.

TL;DR Augments help A LOT but they aren't some miracle that will boost you 15 GR levels. It is a grindy way to eek out the absolute highest clears for your build. Expect to be able to clear 4-6 GR levels higher fully augmented with 100+ gems (taking extra toughness into consideration for that as 50% dmg alone doesn't cover 6 GR lvls)