But any mission involving humans is likely to carry a large amount of water beyond the crew's personal needs, because it makes such a good radiation shield. So presumably the same water would be used for cooling the reactor.
A 3 MW reactor puts out a hell of a lot of heat, and without the benefit of air-cooling in space, I'm not sure what exactly you would do with all of that waste heat. Consider how massive the space shuttle orbiter's radiators were (they are on the inside of the cargo bay here: http://i.stack.imgur.com/Flgzb.jpg ), and all of that is only capable of shedding waste heat in the amount of ~6 KW! We can put a much more capable reactor into space than we can possibly cool, so we haven't bothered. Cooling is the real problem. The total mass of the radiators and the structure required to support them ends up being way more than the reactor itself.
So for good long distance transportation in space, not only do we need a working, efficient emdrive, but we also need better power generation that is much more efficient from a waste heat perspective. These are really hard problems.
1. Details on submarine nuclear reactors are classified, but five minutes' Googling shows that a reasonable guess for their total mass (including shielding) is 1,000 tons. Meanwhile, the entire payload to LEO of the largest rocket ever successfully launched, the Saturn V, is only 155 tons -- and that's for the entire top stage.
2. Submarine nuclear reactors use water for cooling. Water that is not available in space. Cooling would be a huge problem.
So, existing submarine designs are not practical. You'd need to design something from the ground up that is much lighter, and the cooling system would be entirely different and likely more massive, since you don't have all of that free water available to dump heat into. Instead you're talking massive radiators.