Automation of eq bypass

Yes, its possible if that EQ has an on and off or bypass option. If it does, Just select the envelopes that contorl the bypass or the on and off and set it up to do what you want.

The Sonitus EQ isn't a good candidate for this type of treatment, as it neither allows automating the bypass function nor does it provide a wet/dry mix control. The best way to handle this with the Sonitus EQ is with two aux sends to two busses. Place equalizers on each of the busses and then automate their respective output levels.

You may not need to go to that much trouble, though, depending on how different the two EQ settings are. If it's just a single band, e.g. putting low frequencies in at one point and cutting them back at another, it's easy to automate the gain for one or two bands, making two instances of the plugin unnecessary.

If buying a third-party EQ is an option for you, there are other plugins that do offer wet/dry mix controls that make this kind of thing much easier to accomplish. I've just picked up MeldaProductions' MDynamicEQ, which is on sale now for a mere $27. It excels at this type of application, allowing you to set up multiple EQ settings (up to 8) and switch or morph between them. It also has a global wet/dry mix control.

One avenue you might want to explore with the Sonitus is to set up your EQ Type, Frequency & Bandwidth the way you want, then automate the GAIN for each band you want to control.

Start each band with a gain of zero, then raise/lower it with a steep curve (you might get the odd pop, or artifact if the curve is set to vertical)

In fact, what I'd do would be to record your automation roughly, then go in and fine tune the curve(s) in terms of slope/placement.