You definitely need DC biasing to center your signal around 2V if you are interested in the negative half-wave of your input signal. I guess you'd get some pretty interesting distortion from it otherwise, but also you'd need to add extra circuitry for protecting the input from negative voltages, so you may as well do the biasing properly. This is relatively straightforward, by putting two high value resistors in series between 3v3 and GND (e.g.: 68k and 100k) and connecting the midpoint to the analog input. This is assuming that your input signal is AC-coupled, or you'll need to add a series capacitor as well. If the amplitude of the incoming signal is likely to be larger than 4V pk-to-pk, you'd need some schottky protection diodes, or at least a large enough (1k?) series resistor to limit the current into the IC.
You can do without the filter but - also depending on the high-frequency content of your input signal - this may end up being quite noisy. Anyhow, worth a try as the components and effort needed to try it out are minimal.
