Azeroth's nature is much more tame than Draenor's, the Botani themselves are what happens when you let spirit energy get out of whack. Azeroth has a world soul so much of the spirit goes directly into fueling it with nutrients, this results in low spirit levels but hostile elemental forces because they are all trying to get a piece of what is a more-rare resource. Draenor didn't have a world soul and the spirit energy got so out of control Aggramar himself had to create the Breakers to combat it for it to even be hospitable to regular life. Even after that Draenor still has bountiful amounts of spirit which is why the elementals are pretty chill there, and then you got things like the Botani that could get out of hand if left alone for extended periods of time again.
It's hard to say how being on Azeroth could impact the Botani, but it's probably safe to say they could mellow out and potentially be capable of reason. They are supposedly pretty intelligent, but not civilized by any means. With a lack of spirit to fuel their previous way of life I could see them creating allies with one of the factions for their own survival. On the other hand they could be desperate for Azerite which is probably overwhelming with spirit energy due to being Azeroth's lifeblood, so they might do anything they can to get a hold of it to continue what they were doing previously.
While it would be neat to see both Saberon and Botani as allied races, I don't think they are much more than savages currently. I think a more realistic outcome for them running off at the end of the Mag'har scenario would be if we see a Barrens warfront sometime during BFA, with Botani and Saberon having camps/settlements similar to how there are forest trolls and ogres all over Arathi and are targets of quests/rare spawns for items and such.