The auto speedbrake function on the 737 is just that...a function. As continually said here, it can malfunction!
In the heat of the moment during any RTO there is always potential for something to go amiss, although in my experience it is usually during the later stages when the aircraft has finally came to a stop and malfunction diagnosis, followed by memory items and a possible resultant evacuation occurs (ie NOT stowing the speedbrake lever or ensuring flaps have reached 40 degrees. This has all been observed (thankfully only) in the simulator.
To me the PM call 'speedbrake' or 'no speedbrake' is worth it's weight in gold here. Immediately after any touchdown and equally as soon as an RTO is initiated.