What is the effect of Saturation on a Ferrite Bead Inductor?
Two primary things happen when saturated: 1) the effective permeability drops so the relationship between amp x turns and the field is no longer linear 2) you get "field popping" which describes the fact that the core can not longer contain the field and moves outside of the core.  You van get very high EMI/RFI in these situation because of the huge disparity in in relative permeability.  The field has to rapidly expand (outside of the core) to compensate.

In the case of the ferrite beads, you will lose filtering but in the circuit above only displacement current flows (because of C6 and C12) so only very extreme spikes will cause any saturation.