What's the purpose of a ferrite bead inductor on this circuit?
Yes, it's basically part of a low pass L-C (or R-C for high frequencies) filter for the analog Vdd on the chip (with C9).  Ferrite beads act like very low resistance (&lt; 1 Ohm) for DC, inductors (several uH) for low RF frequencies and they act like resistors (hundreds of ohms to 1K or more) for frequencies in the 100MHz range. 

Ferrite beads are normally specified in ohms in the resistive region (relatively high frequency- usually 100MHz) where they are very lossy, but they have an inductive region at lower frequencies. Note that care must be taken with this kind of circuit that noise inherent in the supply does not resonate at high Q with the ferrite and capacitor or the bead may actually result in more noise on the power rail. A good reference on beads can be found here. This sort of thing can cause all kinds of grief if the SMPS noise is (or has a harmonic) close to resonance and it changes with loading or input voltage  or temperature to move in and out of resonance. 



If you simply omit it the chip will not work properly since there will be no power supplied to Avcc. If you replace it with a short, the chip will operate normally, however you may see somewhat higher noise on ADC readings and possibly other subtle effects on analog performance.  

R33 may have been a thought to allow for a ferrite bead in the analog ground (usually not a good idea) or it may be used as a net tie to enforce a single point connection between the analog ground nets and the ground.