Yes you can do that. There is a script command for setting a random variation on the sizes of particles -
SetPSScaleVariation <partSysName> <low> <high>
You enter the name of the particle system, then a low and high multiplier. The multiplier acts on the particle sizes that you set with the SetPSParticleSize command. So this command
SetPSScaleVariation "my system" 0.5 2.0
would randomly vary the particle sizes by one half to two times what you set for them. For a given particle, the scale factors apply to both the initial and final widths and heights of the particles, so the ratio of final size to start size always remains the same for each particle.