@Ingolifs' answer got me
procrastinating thinking further.
What you're asking about is a mass driver space station in low earth orbit that a payload or ship launched from earth can dock with, and then be propelled into deep space.
The delta-V needed to go from LEO to an escape trajectory is about 3 km/s, and to go from there to a Hohmann transfer to the outer reaches of the solar system requires a further 5 or so km/s. I'm sure a mass driver could be made to provide such delta-Vs, though it would have to be rather long in order to not smush the payload with its massive acceleration.
One big problem I see is Newton's third law. Due to recoil, the orbital mass driver will have the same momentum backwards as the craft will have going forwards. This means its orbit will be altered...
The railgun's orbit will be of course altered, but if the rail gun is long enough to minimize acceleration for payloads like living humans, it will be subjected to some complex torques as the projectile accelerates along it and pushes it backwards. These will set this long structure rotating, and may even bend it under these transverse loads and tidal effects, unless it is made strong and heavy (and expensive) enough to withstand this.
Tumbling of something very long, heavy, and solid in LEO also means drag, reentry, and danger to folks on the ground, so you'd like to keep it re-oriented fairly nose-on to minimize drag as quickly as possible.
Is the best shape a straight line, or should it be somewhat curved in order to track what the spacecraft's trajectory would look like as it accelerated from circle to elliptical to hyperbolic tangents?
I would suppose that the rail-gun-as-reaction-mass would have to be much heavier than the projectile, but it isn't realistic to treat it as infinitely heavy.
With some suitable assumptions of length and mass and target (Moon, or Mars) what would be the ideal shape for this object in LEO?
note: I've added the math and physics tags to indicate that I'm looking for a quantitative, reasoned answer, not just something like "it happens so fast that it wouldn't matter" type of hand-waving. Thanks!