Must admit I've been toying with a similar idea, except at interplanetary scale.
The huge advantage is that you are free of rocket equation constraints. As all the energy is delivered externally, you don't have to hand wave about Bussard Ramjets and the like. The presence of a catcher is also required, unless you are going to try and carry all the fuel for the slowdown phase, which pretty much defeats the point. If you are doing that then you might as well have a detachable 'acceleration phase' stage.
So what are the problems:
1) As mentioned above, massive sustained acceleration, unless you have an amazingly long rail gun assembly. In a zero-g environment, a structure that is 100s of km long is not impossible. I would presume that in a zero-g vacuum environment a barrel would not be required, if your magnets can keep the projectile going straight. Indeed, at the speeds involved a physical barrel would just be a hazard.
For the payload, you'd have to go beyond acceleration couches. Think full immersion in a fluid (no air gaps, even in the lungs or ears); possibly freezing solid. You want to avoid any density contrasts within the ship in the acceleration/deceleration phases, to allow for the 100+g loads. 898
Once in cruise phase, you could come out of vitrification.
2) Safety - Well.. you've accelerated a ship weighing hundreds of tonnes or more to, perhaps, 1000km/s. Going by the kinetic energy formula, e = 0.5mv^2, that would be ~10^17 J According to the Wiki, that's about a Tsar Bomba). So if anything goes wrong and you hit a planet (never mind a KBO) you will leave a noticeable dent. Even under good conditions, your catcher has to dissipate that amount of energy in a very short time. You'll need some very, very big capacitors.
3) Practicality - As long as the system is reliable and the energy requirements are solved, then it avoids sending huge fuel tanks out on long, tedious orbits. So in many ways better than chemical rockets or solar sails. It also requires some form of hibernation/sleep tech, as above.
4) Orbital Paths - You would probably need some form of adjustment onboard, but the calculations would be pretty trivial. You'd also want adjustment thrusters in case space junk was detected en-route, as collisions at cruising speed would be very very dangerous. 947