Well, provided the mechanisms were geared for it, there's not reason why not. Although, for really complex organisms, it's very likely that the 'clone' wouldn't so much split off, as for an embryonic tissue 'pod', like an egg or something, to develope from identical genetic information and then grow independantly of the 'parent' organism, either internally or externally. But yeah, splitting can work for complex organisms just as well as simple ones.
The trick is to remember that organisms which use splitting as their primary means of reproduction, usually take a lot longer to evolve any fixed traits. However, when they do, they tend to speciate much more quickly, sometimes in single generation.
Most simple organisms make up for the lack of mutation rate by having massive reproductive rates, allowing them to produce many more generations in the same span of time as most more complex organisms, so overall, they're about equal. Higher organisms, like vertabrates, would have an appallingly slow rate of mutation if they cloned, so a species would be basically stagnant in that ragard.