Can vent plumbing be behind a double wye?
Around here the answer would be no. Our plumbing inspectors won't pass drain installations where a connection to a common drain line comes before the vent. The one exception would be the toilet, which can be wet vented to another fixture.  The problem is that the air admittance valve is too small to vent the toilet, and the height of the toilet trap is above the height of the shower drain.

Keep in mind that local mileage on this stuff varies wildly, so I'd run it by your local inspector. Also, don't know if this is just a mistake in the diagram, but the wye connection to the cast iron pipe is upside down.