The series inductor seems to be inviting disaster. Inductive loads on regulators can cause them to oscillate. You'll never see that in the datasheet, only the capacitive quadrant is specified -- if they give a region of stability at all, which they often don't. (An extreme example is the intentional use of a LM317 -- a notably stable regulator otherwise -- as a Hartley oscillator for medium wave radio. It's been done!)
A ferrite bead or choke, between caps (a pi filter), is fine, and yes, can be used to help reduce white noise from the regulator, and switching noise coupled from the source. Better to put the filter in front of the regulator for the latter case, and better to use a regulator with reference filter pin for the former case.
Tim