No. The dynamics of increasing speed on a geared bike, regardless of whether you have a motor to help or not, remain the same. You shift into the higher gears to accelerate speed, and downshift to climb hills.

My newest ebike is a manufactured one, not a conversion like my first. The motor is integrated by the manufacurer into the crank set and is programmed to engage when pressure to turn the pedals is consistent. It will ignore simple singular turns of the pedals as is often the case for hand moving a bike around, readjusting position on the bike, etc. The motor "waits" until a firm continuous (at least one revolution) turn of the crank is made before gently engaging. By the second to third pedal revolution the motor will release significant torque at a quick, graduated level to help move the rider along without being abrupt or disruptive. The torque is disengaged instantly if pedal pressure creases. When pressure is again applied, it again takes at least one full revolution of the pedals for the torque to reengage. The amount of power released to the torque is based upon my selection of assistance I chose via my bike's control panel.

The results are extremely smooth: subtle at the onset, powerful afterwards. The amount of torque released as the rider pedals forward is based on how consistently the rider applies pressure to their pedal stroke. I have discovered the bottom end torque starting out is the one felt the most (by me, at least). The feel of the torque is more subtle as speed increases. It doesn't seem to continuously "build" per say, but rather becomes an unnoticed background influence as you achieve the speed you want.

The torque flattens the hills, removes headwind, and helps start the bike easier and more smoothly than a non-assisted bike. Your gears will still help in climbing hills, but that's pretty much the only time you would need to downgear. If you want to go faster, then gear up. Your torque remains consistent in the aid the motor gives, it just becomes more efficient when your gearing is appropriate for what you want to achieve. I also have the option with my bike to choose no assistance at all. In that case, my ebike becomes just a quality aluminum bike and moving it along down the road is all on me and my efforts (and use of the gearing) alone.

I know this is far more information than you asked, but hopefully it will give you a better idea of how an electric bike motor is programmed to work in tandem with the human motor. Honestly, it is one thing to describe, it's another to actually feel underneath you how your bike "comes alive" to partner with your efforts, rather than being a passive thing that just doesn't care. If you've never tried a well designed, manufactured ebike, you really should. It might open your eyes and mind to a whole new cycling experience