In my eyes (or ears) the saturation is just a way to emulate the behavior of true analog synths when they encounter "over driven" sounds, since the Virus has lots of spare bus overhead to let you add more and more dBs without resulting in distortion (I mean internally - the DAC or your DAW may still produce distortion for output over 0dB).
Now, the actual change or distortion of the original OSC sound depends on the printed circuit design, and exactly how the transistors interact in their saturaion and cutoff zones, which may change even from batch to batch of the same model... But I guess this is why more then one saturation option is provided (except for the analog 1 to 4 pole moog model, for which I guess the saturation is modeled as well...?). From my experience, the virus's saturation decision algorithm is very simple - once the sound is over a certain threshold, the chosen effect is applied in a level that is proportional to how louder the sound is from the saturaion threshold (probably derived from some RMS calculation of blocks of sound data).
You can hear it come into action in either of the following ways:
- Use a very very long attack time so you can clearly hear when the saturation kicks in.
- Make the OSC velocity very influenced by the key velocity (if you tend to strike the keys forcefully, make it inverse!) and play notes in different velocities. With the right patch, you will notice that sometimes, the sound is not saturated all the time.
The weird thing is that some of the saturaion effects are purely digital, such as bit reduction, which has nothing to do with analog modelling, but, hey, that's what's so good about DSP based synths, isn't it? Once you add a "processing block", why not exploit it to its fullest?
Regarding the interaction with the filter, it depends on the routing scheme. The saturation block will take the input from its left and send output to the right. Whatever filter you have to its left will have its output saturated and then filtered by whatever filter there is to its right. Since many of the saturation effects are types of distortion, which create new sub-harmonies from existing ones, changes in resonance, especially when self oscillating, will have a dramatic effect on the outcome.
On the other hand, there are some effects such as low pass, that reduce the velocity of the sound. I guess they can be used as some kind of compressor, affecting the sound dynamics.
Hope this helped.