Yes, that's why a single eruption can have a noticeable effect.
Stratospheric water may also set the upper limit on how many launches to orbit can be done per year, since all the propellant consumed in or above the stratosphere makes water that ends up in the stratosphere.
You would not want to make so many launches that it perturbed the climate, due to water vapor increase in the stratosphere. We are nowhere close to this happening yet at current launch rates, btw.
Stratospheric water may also set the upper limit on how many launches to orbit can be done per year, since all the propellant consumed in or above the stratosphere makes water that ends up in the stratosphere.