Ferrite beads are lossy inductors, at frequencies below e.g. 10 MHz they behave purely inductive, at higher frequencies more like resistors.
LC filters in power supply always bring up a risk of oscillations with load transients, depending on the LC resonance frequency, characteristic impedance, load impedance and supply current waveforms. In case of doubt, you should calculate and/or simulate the expectable behaviour of the filters.
The point of placing ferrite beads near the EMI source is to keep the interferences from spreading allover the board, being radiated by power supply lines and planes. This can only work if low ESR/ESL capacitors are directly bypassing the switching currents at the chip.