This isn't the answer you seek, but let me observe merely
that if you allow extra balls and if the table width is an
integer number of balls in each direction, then we may
imagine a cross pattern with the cue ball at the
intersection.

    /------------------\
    |         O        |
    |         O        |
    |         O        |
    |         O        |
    |OOOOOOOOOCOOOOOOOO|
    |         O        |
    (         O        )
    |         O        |
    |         O        |
    |         O        |
    |         O        |
    |         O        |
    \------------------/

Under your idealized physical interactions, it seems that
the cue ball cannot move, since the forces acting on the other balls are all transverse.

Probably one can also imagine other highly-packed
arrangements.