I am not much knowledgeable about switching supplies...but as far as I know, inrush current is because of the filter capacitor. When completely discharged, the capacitor presents an almost shorted load - this is reflected back via the rectifier diode to the transformer. So when powered up, the transformer's secondary sees an almost dead short (and therefore a very large secondary current) for a few micro-seconds while the capacitor charges up. The large secondary current draw is reflected back into the primary causing the typical "dimming" of lights when the power is applied. This is most apparent with transformers with VA ratings (or total VA, if using multiple transformers) of 300VA or higher.
For an SMPS, if the power is, say 500W, that implies a 500VA (or more) load placed on the mains and the same effect is mimicked when the SMPS is switched ON. I'd reckon the effect to be the same as if a 500VA transformer with rectifier and capacitor is being powered up.
If you place a choke (or inductor) between the rectifier and the filter capacitor (i.e. a choke input filter) it should help with controlling the current surge when the capacitor is completely discharged - in effect the sudden current surge will be suppressed by the choke. Not sure if a PI filter will be better than a choke-input filter.