In D&D5, 'Versatile' means that the weapon can be wielded one-handed or two-handed. The two-handed wield option inflicts more damage.
BG3 has, so far as I can see (I've not tested every combination), implemented this, so the answer is yes.
Sadurian, this is currently not accurate, I'm sorry. It's not true at all.
Currently there is *NO WAY* to use a Versatile weapon one-handed without also equipping a shield - no way to use a versatile weapon one-handed, with your other hand empty. It will always be used two-handed if your off-hand is empty, and use the higher damage die.
If there IS a way to use a versatile weapon one-handed while your off-hand is empty, then the game does not make the mechanic of how to do so clear or visible; to the extent that everyone here believes it cannot be done.
(Certainly, for the fighting style, a shield is acceptable, and you don't need the hand to be specifically empty (which is accurate despite the description saying otherwise)... but we should still be able to, because there are other features that aren't in the game yet for other subclasses that do want an empty hand.)
Spears and Quarterstaves are meant to be versatile, but are not, but I'm sure that's been reported on by many people already.