First, electric thrusters require a lot of electricity to produce a little thrust. For example, according to this source, a Hall effect thruster typically produces about 50-70 mN per kilowatt. If the technology scales, you'd be talking about 50-70 newtons per megawatt of electricity. Other electric thrusters might produce more thrust per megawatt, but we're not talking about a dramatic difference.

To achieve bouyant lift, you have to have enough atmosphere to displace. Once you start to accelerate, you start producing drag which slows the already low rate of acceleration. A kilometer long aerostat filled with pressurized living quarters, power sources, and a propulsion system is still going to have a mass of many tons. Acceleration = force / mass, and the force is going to be low.

Suppose you leave the high altitude docking station at the break of dawn and begin thrusting. If your acceleration is 0.01g (and I think that's being generous), at the end of the first hour, your velocity would be about 353 meters/second (about 790 MPH or about Mach 1.3-1.5 at that altitude), except for drag. As you accelerate, drag increases with the square of the velocity. The net result is that acceleration decreases as you increase velocity. Given the very large surface area and low thrust, it wouldn't take very long before acceleration becomes essentially zero because drag will be equal to the thrust. There isn't any way around this because this idea calls for staying in the atmosphere to generate lift until you have a velocity high enough to go into orbit. This seems very unlikely to me.