Logia will have awakenings like any other fruit. It may have been shown as early as Marineford.
When Whitebeard impales Aokiji, someone is heard shouting that “he stabbed him with haki, is he dead?!” Aokiji, impaled, responds “don’t be stupid.” (One of the earliest clear references to haki in the story)
Logia awakening may simply be a true and permanent transformation into the element that also grants the ability to heal or regenerate damage and access to more powerful expressions of the ability, even regenerating or resisting damage from haki-infused attacks. Aokiji was impaled at MF by Whitebeard using haki with no permanent damage. Monet, very similar fruit but too weak to have Awakening, would have died if Zoro cut her with haki.