Will I be able to use the Unifix tool to repair a floating floor that was glued on the edges?
It's not fun or easy, but it can be done.  Good answer was provided here How can I replace a board in floating wood floor?:

From the previous answer:


  You'd have to treat it like a hardwood floor t&amp;g repair:
  Run a circular saw down one side, staying away from seam at least the thickness of the tongue, with depth set to board thickness.
  Repeat #1 along the other side.
  Connect the top and bottom cuts across the board, either with a chisel or OMT (Oscillating multi tool).
  Carefully cut into corners to free the 4 border pieces, as necessary. They may just pry out.
  Trim the bottom half of the groove off. (I like to use a table saw and fence). You should be able to wedge it in with the tongue intact, though a small bottom bevel might assist it.
  Sparingly glue along edges of existing tongues and the new board edges and weight it down, as necessary.