personally I don't think going anywhere near the autopilot on a light weight 737 missed approach is a good idea, as I understand it (I may be mistaken) hitting TO/GA gives you 1-2000ft minute rate of climb, engage the A/P & A/T and now it's going to go for full whack.... in a light weight 737 that is imho recipe for disaster, alt cap, wrong speed set, loads of power off and on etc.... personal preference is to hand fly it all until clean and levelled off and then engage automatics, I put them in sooner though if heavier and not just below the Missed approach altitude,
it would be really interesting to know more about the MCP modes etc e.g. had they pressed the TOGA switch or was FD giving guidance to their approach etc etc.... so much conjecture without all the facts.