Well, you wouldn't haul a full assembled reactor into orbit, I wouldn't think.
To properly construct a ship capable of using the size drives and reactors they're talking about you'd have to have an all new space station crewed by a lot more than 3 people to build it.
I mean even if it can make the trip to Mars in 40 days or whatever that's 80 days both ways plus the time in orbit while to do the science and wait for the return window to open up. So you're gonna need a ship with life support capable of keeping the crew alive that long. Which is a complicated prospect. Some of the stuff they've been cooking up long this line looks overly complex, which as a wise Scottish engineer once said, "The more they tech up the plumbing, the easier it is to stop up the drain." Or more correctly to quote Kelly Johnson,
"Keep it simple, stupid".