This is a 3-tray 1UP rack, which means it is a double tray with a single add-on (you can add one more to make it 4 trays).
In the 3 tray configuration, I have only opened the trunk with the rack moved to it's middle position (not fully folded to the car, but not in the third position for loading). There is a lever at the bottom of the rack that allows you to move it between these positions. The adjustment lever is a bit cumbersome in location. They also sell an extension adapter for the lever to make it easier to adjust. I don't think the 3 tray configuration will have enough room to open the trunk in the folded state.
With bikes on the rack, the trunk will only partially open, then it hits the handlebars of the first bike. You do have about a foot of clearance to get partial access to the trunk.
You can also swing the fully loaded bike rack down to the ground to access the trunk. In the 3-tray configuration, this gets difficult because the lever is down near the base. With the lever adapter, this would be easier.
Alternatively, lay the back seat down to access the trunk space.