If you accelerate them, and then use microstepping when they are up to speed, they can be much smoother and quieter.
No, you want to do the opposite. At low speed you want to use microstepping in order to reduce the energy wasted by the mechanical "ringing" introduced when fullstepping (which obviously also reduces the noise), reducing resonance issues etc. As the speed increases you can (if needed) switch to full-step mode since the benefits microstepping provides sort of dissapears.
If the motor does its work at a speed of more than a couple of revs per second not much is gained from microstepping it (except during the acceleration/deceleration phase) since the inertia will tend to smooth out the vibrations at that sort of speed anyway. Sometimes though it's impossible to get up to speed using full step mode since the vibrations at low speeds can cause the motor/load to resonate so badly that it drops out of sync.
Finally, it's not clear if you by "noise" means the noise caused by the vibrations of the motor or the noise from the current control chopper on some drives. Some drives are totally silent while others makes the motor "sing" and "chirp" at rather high frequencies.
Bottom line, use modern microstepping drive or switch to a real servo motor with feedback.