Can all pass filers have a pole/zero at the origin of the root locus
a delay is also an APF of sorts.  it passes the same magnitude and it affects the phase (in a linear manner w.r.t. frequency).  a delay of one sample has transfer function

$$ H(z) = z^{-1} = \frac{1}{z} = \frac{1}{z-0} $$

which means there is a pole at $z=0$.  and it is true that $\left|H\left( e^{j \omega} \right)\right| = 1$, so it's an APF.

so, if the remaining pole/zero pairs are at reciprocal values this extra delay changes the phase of your APF a little, but not the magnitude response, so i think, strictly speaking, that it's still an APF.