Seems to me that they already answered that one...
Not to the fullest. There's two possibilities here. Let's go over them.
Option 1: You unlock the Nar Shaddaa through your Legacy with credits or cartel coins. Now every character in my Legacy can open their own Stronghold on Nar Shaddaa that each character can customize as they see fit, with decorations that can be claimed (like collections) that are also unlocked Legacy wide. This way, my Bounty Hunter can make a bar/club out of it, yet my agent's stronghold can be totally different, more like a secret base.
Option two: You unlock the Nar Shaddaa through your Legacy with credits or cartel coins. You can then decorate it with items, trophies and furniture that you unlock Legacy wide. However, you can only do this ONCE. So each character from your Legacy will walk into the same Nar Shaddaa palace, as you, the player, decorated it, regardless of class. This holds true for every stronghold that you, the player, unlock. They're a shared instance that can be decorated once but will be accessible to all characters on your Legacy.
Option 1 is what I hope. Option 2 is what I dread.