The Go Out rule says if you discard your last card that can't be played ends the round. You can't discard to end the round if the card is playable and become a "floater" or in "limbo" till you're able to go out with the proper discard. Now, if you discard a "SKIP" card, does it end the round or put you as a"Floater" still?
Under the Floating variant, if you are floating and you draw a Skip, you must use it and the round is not over.
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.