Does the rate of movement of ions in a salt bridge affect the total voltage produced by a Galvanic cell?
Voltage measurement is ideally a zero current process. Therefore the details of the ions in the salt bridge and their movements will not be an issue.

In reality, voltmeters do flow some current to measure the voltages. Yet, these currents are so small that in any self-respecting salt bridge, there will not be an issue. If your salt bridge was broken for whatever reason though, then your measurement will be completely incorrect. Most voltmeters will give you an overload in that case.