Can F2/HF be separated using acid/base solutions in series?
The answer is no, because as you remark $\ce{F2}$ will react with water and produce $\ce{HF}$.  So it is not the case that $\ce{F2}$ passes through unreacted.

I'm puzzled by this sentence: 


  Despite the Method not mentioning F₂, it commonly produces data for both HF and F₂


Can you clarify what you mean by "it produces data"?