I'd certainly think so. The skies must be full of uninteresting derelicts, and Khan's ride would be among the sorriest. Nothing would indicate anything of worth aboard; why should Admiral Marcus' men stop and investigate?
Really? Those were Kirks orders?
Apparent from many episodes of TOS. As far as space explorers go, he's much like Doctor Who or Spaceman Spiff, having adventures for the sake of having adventures - there's no clear logic to him e.g. trying to stop one asteroid out of thousands in "Paradise Syndrome" from hitting a planet in the middle of nowhere, other than some sort of perverse curiosity to see if it can be done.
Curiosity like this would greatly benefit the UFP as long as their Starfleet can afford the time and effort spent - somewhere way down the line. It's difficult to see how it could benefit S31 in its narrower-scope quest to strengthen the defenses of the UFP, though.