What defines precious cargo? Satellites and astronauts seem to do alright going into space attached to a giant rocket, but I will admit I'm not well versed on the forces created from a electromagnetic launcher.
So here's one way to think about the accelerations. To a first approximation, you need the same total change in velocity to go from standing on the surface of an object to be in orbit at a given altitude. You can choose to spread that change in velocity over any given time and distance interval (those two terms are linked). So if your mass driver accelerates your payload to final velocity in 1/10th the time (and more or less distance), you will get 10x the acceleration.
So the forces you would be subject to will be more or less directly related to how large of a mass driver (in terms of track length) it is relative to the mass of the object you are leaving.
Rockets are actually relatively gentle in comparison, generally <3G for humans. This is because you can apply constant thrust the entire way to orbit (>~400 km on Earth)
With a Mass Driver, you can only apply acceleration for however long your driver is, so you have to get up to speed in a much shorter distance. If you build a 4km driver (length of Heathrow Runway), you have to get up to speed in 1/100th the distance causing drastically higher accelerations.
(note, some poor assumptions here because horizontal distance =/= vertical distance, but the general idea is correct).
So here's one way to think about the accelerations. To a first approximation, you need the same total change in velocity to go from standing on the surface of an object to be in orbit at a given altitude. You can choose to spread that change in velocity over any given time and distance interval (those two terms are linked). So if your mass driver accelerates your payload to final velocity in 1/10th the time (and more or less distance), you will get 10x the acceleration.
So the forces you would be subject to will be more or less directly related to how large of a mass driver (in terms of track length) it is relative to the mass of the object you are leaving.