By the looks of it they seem to get the Eyebeam & Blade Dance reset baseline by level 52.
Darkness, however, stays a 5 minute cooldown.
You can look it up yourself in Dalaran’s DH Video called " Demon Hunters In Shadowlands Alpha! First Impression"
He goes through pretty much all the nerfed abilities starting at minute 4:55
Blade Dance has no longer dodge as a component (which apparently rumors to be back already ingame, though)
Blur gives 15% less damage reduce
Darkness has a 2 minute longer CD
And at 3:55 you can see Metamorphosis giving you 0% Leech without Soul Rending, effectively nerfing the current Leech by 10% overall if you still pick that talent.
BfA Meta gives 20% Leech baseline, 10% passively through Soul Rending and another 10% in Demonform.
Shadowlands Soul Rending gives 5% Leech baseline and 25% in Meta, nerfing it by 10%.
The good changes to Havoc so far in Shadowlands are:
Immolation Aura baseline, although without its fury regenerating component. Which means you will pick the new talent in the second row (that currently is Immolation Aura in BfA) to get fury with it.
Pretty much changing nothing about the Spec at all. You are the same demonbat fishing for Mana Rifts - just extremely nerfed while nearly all other classes get so much stuff baseline.
To come back to your question:
Pretty much, yup. They also buff Demonic Appetite heavily by baking the “Eye of Rage” Azerite Trait into the talent, reducing Eyebeams CD for each Soul Fragment by 2 seconds, up to a max of 15.