Yeah as i recall he (when first found by kirk and spock prime) seemed to say the dog was "temporarily missing" as if he felt that in time he would recover the dog.
now that may or may not happen, i guess if he mis-calculated and the transport went wrong in the t-Dimension then later at z,y,z,t the dog could rematrialize but that would mean that some how the reciving transporter would need to get a signal and return the dog to the proper form ??
the other possible case based on some prior trek "cannon" is the dog is stuck in a loop-ing pattern buffer...
in TNG there was a "final goodby" to the TOS Mr. Scott where he "saved" himself that way and the TNG crew got him out.
recall that one??