No. It won't.
The devs have a new Unified Humanoid Model. Forsaken, Orcs, Trolls, Humans, EVERYONE uses it so that they can have the same attack animation for Mongoose Bite across all races and have a -vastly- easier time adding new races since the skeleton is pre-rigged. It's -why- we're getting 6 new races.
The Nightborne and the Zandalari currently use the old Night Elf skeleton because it was easy to use for the rigging, but they'll need to be migrated to the Unified Humanoid Model so they can have Charge use the new shoulder-rush animation rather than having to remake that animation for each of the new races.
It's likely they'll share some walk/run/jump/die/autoattack animations with trolls or nelves or something, and have some new versions of other ones, but they're not going to be using the Old Nelf Skeleton in BfA.
Velf/Belf is totes likely though because they ARE Belves. They're already rigged on the new humanoid unified skeleton so they don't need to make a separate set of animations for the same "Warlock Casting Stance" or whatever. Though we do also see them floating in the brief previews we -have- of them, so they might have new run/jump/die/autoattack and such... we'll have to wait and see.