I think that the dead could travel to Azeroth via the portals in Oribos.
I don’t think we’ll see it anytime soon because the situation in the Shadowlands is too dire for anyone to really leave. The Kyrians are maintaining business as usual, for example, or at least as much as is possible given Forsworn interference. Maldraxxus is in a state of Civil War. Maybe Draka wants to go to Azeroth to find out what became of her son, but she has a duty to the Shadowlands. Revendreth is in a state of upheaval with those loyal to Denathrius still causing trouble, and the anima crisis meaning every Covenant is in dire need of Anima, and Revendreth is the best place to source it. Ardenweald is collapsing with the Night Fae forced to use Triage to save as many Wild Gods as possible.
Should things stabilize somehow, I could see denizens of the Shadowlands going to Azeroth. The Night Fae are inherently curious, and I imagine the theatrical play about Azeroth would make more than a few quite interested in seeing the world for themselves. I could easily see Theotar being a tourist. Honestly, I’d pay for the next lore book to be written from the perspective of Theotar touring Kalimdor.
“Ah, Orgrimmar! A little bright for my tastes, but so lively! The people of this city are hardy and bold, and not easily given to despair or defeat. The city itself is charmingly rustic, and most endearing, yes! Why, I would go so far as to say I could see myself visiting more in the future! They have a delightful place they call the Cleft of Shadow. What this city needs is a tea parlor, and I would be most happy to supply the good people of Orgrimmar with tea in the Cleft of Shadow! Tubbins and Grubbins absolutely adore it.”
“As I traveled through this, ‘Dustwallow Marsh,’ on my way to visit the remains of a fallen city called Theramore, I could not help but to compare it to Revendreth’s own Endmire. Tubbins and Grubbins felt the same, and used several infused rubies to light our way, although I am not thinking it was quite necessary. Theramore itself was a wonder to behold! My, the swirling colors, so bright and vibrant, underscoring the sadness of the destruction that befell this place. Alas, death is as inevitable as sin, but that is why the Sire made us. Perhaps some Sinful souls yet remain? There was a promising little hovel we passed called the Swamplight Manor. How quaint that the humans who dwelt here referred to it as a manor. So very droll.”
“When I first entered Ashenvale, for a moment I thought I had somehow found myself in Ardenweald! How truly remarkable, I thought, to find a forest in the mortal plane so similar to our own forest of eternal winter. I cannot say the natives there were particularly welcoming, however. Why, one brazen cur shot at me! Me! Her arrows pierced my finest parasol! These Night Elves are most uncouth, and I shall make sure to register a complaint with their superiors. They seemed to think I was invading. The nerve! I produced the parchment stating I was an invited guest on a tour of these lands. As if I, Duke Theotar, would ever stoop so low as to set foot somewhere without invitation! I was so cross I didn’t even invite them to tea. That will show them!”