Answer
Assuming the variable region which binds to antigens is undamaged in this process, the clipped-off end could theoretically still act on the intended antigens.
Work Step by Step
It is the Y-shaped end of the antibody that binds to antigens and neutralizes them, not the heavy chain connecting it to the cell membrane. Though some free-floating antibody ends may or may not be as effective as those on an active B cell, they could potentially continue to work just as well.
