GEO via Construction Orbits
Hohmann to GEO
The usual way to reach GEO is a launch into an elliptical Geosynchronous Transfer Orbit (GTO) followed by an apogee insertion burn. GTO starting from launch loop altitude (80 km) to GEO will start with a perigee velocity of 10346 m/s (or 9875 m/s relative to the rotating Earth) and arrive at GEO radius (42164 km) with a velocity of 1585 m/s, 1490 m/s slower than 3075 m/s circular orbit velocity at GEO.
Escape velocity from GEO radius is 4348 m/s (in any direction, though downward trajectories at any velocity will impact the Earth). Exhaust plume atoms leaving the vehicle at less than escape velocity, but faster than atmosphere-skimming velocities, will orbit the Earth, possibly for a very long time, until they intersect other atoms (or artificial satellites) in orbit. Above 20,000 km radius, there is only a thin smattering of hydrogen, so exhaust plume molecules may orbit for decades or centuries until they hit that.
This diagram describes a "velocity space" around a point in physical space above the Earth.
A particle with a small tangential (horizontal in the diagram) velocity will be at the apogee of a slow orbit, with a perigee inside the atmosphere. Vertical velocity will bring it to the atmosphere sooner, and the orbit can have a little more tangential velocity and still graze the atmosphere.