"Do I Need To Wear a Bra With My Underbust?"
Overall, the answer is no. Not unless you generally don't mind going braless, whether because you prefer to be without a bra, or your bust is on the smaller side so you don't require the support a bra provides, or you've had your breasts augmented, which generally keeps them in their set place with or without a bra.
But for those of us who prefer to the assistance and support a bra provides us with, you will find that an underbust simply will not provide the same degree of support.
Though you may find that when you are wearing an underbust, and you sit down, the top edge of the corset will sit a bit higher pushing the bust up, this is not at all the same sort of support that your bra gives you.
As obvious as it sounds, an underbust does in fact go under the bust, vs. a bra which covers the bust providing support both from the band that sits beneath the bust and from the cups or bonnets which go over the bust.
So there you have: generally speaking, and underbust cannot substitute a bra but at the end of the day going with or without your bra, is a matter of personal preference.
Happy lacing!