Carm, I like you, but no it didn’t and here’s why:
1st and foremost, and this is a big one; many members of the Horde are still incredibly skeptical and distrusting of Sylvanas after the Wrathgate incident, regardless of whether or not she was responsible, it was still orchestrated out of her city by her people. An average Orc, Tauren, Troll, or Blood elf member would not be so quick to accept someone who they have never trusted from the beginning, and even less so after a catastrophe like that which may have resulted in the death of beloved friends or family members.
2nd, she has a history of disputing, and at times, disobeying authority. Like during the Gilneas campaign in which she disobeyed direct orders to not use the blight. Then at the end of SoO, when Vol’jin is unanimously promoted to Warchief, she shows an unwillingness to follow his orders even though he’s one of the very few people on the Horde who she actually respected. Bad soldiers, make even worse leaders.
3rd, Saurfang and Eitrigg exist and they’re very much alive. Not only that, but they are far more skilled at warfare and leadership than Sylvanas is, having been at it for most their lives. In addition to having more experience fighting the Legion as well participating in the climactic fight against archimonde and his armies during the 3rd war.
4th, who the heck actually “likes” Sylvanas. The Horde mostly tolerates the Forsaken at best, and mostly because they have land we want on the EK, but besides that, have there been any bonds made between Sylvanas and other leaders? Even her former second-in-command, Lor’themar, is incredibly distasteful of her and chooses only to respect her for the valiant commander she was in life, not the monster she has become in death. Heck, the only reason she was even allowed to join the Horde because of a Bloodhoof, ironically enough; Cairne, who saw the Forsaken as fellow outcasts much like the rest of the Horde races, and Thrall and the other leaders heeded his wisdom and allowed it. Not because they wanted something as unnatural or inherently evil as Forsaken , but to give them a chance to overcome their dark nature much like the Orcs once did. Something which after time and again, have failed to do, yet they blame others for their completely justified prejudice and hatred towards them.
5th, Sylvanas leads a nation of undead, she lacks the compassion or empathy to lead a faction of primarily living beings, no matter how militarily adept she may be. Most races of the Horde can’t get shot in the heart with an arrow or have an arm get cut off and be perfectly fine, most races of the Horde can’t survive weeks on end without food or nourishment, most races of the Horde aren’t so fanatically loyal to their leaders that they would compromise their own morals and beliefs. These are traits exclusive to the Forsaken and all undead.
I can name more reasons about how literally anyone besides Baine, would have been more fit to lead after Vol’jin’s death, but I think my point has been made. It did not make any sense for Vol’jin to appoint Sylvanas when there were other people in the room who he trusted more and were more capable of leading the Horde against the Legion than she was.