I'm going to go out on a limb here, but the only way Boeing beats SpaceX to Mars on SLS is if SpaceX closes up shop. First flight of Falcon Heavy is scheduled for early next year and will almost certainly fly in 2018. First flight of Dragon v. 2 is scheduled for November 2018, and will almost certainly happen by sometime in 2019. At that point, SpaceX has all of the parts needed to fly to Mars. Mars missions could be scheduled every 2-2.5 years when the orbits align.
On the other hand, SLS is scheduled to fly to Mars in 2033, with probable delays beyond that due either to program development or Congressional interference. SpaceX would have to miss 5-7 opportunities to fly to Mars and SLS would have to hit every milestone perfectly for Boeing/SLS to beat SpaceX. I just don't see that happening unless SpaceX collapses.
What's that about a mission with a Sikorsky drone to Mars in 2020? I've never heard anything about that. Do you have a link?