It's a stub whether you want it or not
![Smiley :)](https://www.eevblog.com/forum/Smileys/default/smiley.gif)
Specifically, it's a double-open stub, so, half-wave multiples are relevant.
But it's also ferrite loaded, so it should be well terminated, and grounding one side or the other will be fine. Which of course suggests the unbal side.
Probably, the balance is slightly better with it floating, but as that puts some voltage on the tube, it will also affect the radiation pattern or feedline current a bit. (Probably negligibly.)
Tim