Phase 10 Go Out Rule
Under the Floating variant, if you are floating and you draw a Skip, you must use it and the round is not over.

Source:


  If no-one else can lay down a hittable Phase in that turn, only another player playing a Skip or the floater drawing a Skip will keep the hand going.


If you are not using the Floating variant then no matter how you empty your hand, you Go Out and the round ends.