How much energy is lost with a gravel tire compared with a road tire?
I understand that around 20% of the energy while cycling is lost by the deformation of the [tires]

No not really. Rolling resistance will increase linearly with velocity while drag increases with the cube of velocity, so rolling resistance is not a fixed  percentage of total power lost. At higher velocity drag will completely dominate.

use plain tires (no tread pattern) as these tires will get more contact area with the ground, therefore needing less deformation in order to equilibrate the forces (with F=P/A)

That's not completely true. The tire carcase is is somewhat stiff and each tread block contacting the ground supports an area greater than its own cross section area above it. Because the forces are concentrated down trough the blocks the area actually in contact with the road is lower but each block exerts a higher pressure against the road surface.
There is additional power loss through greater flexing of the tire and tread blocks though so there is additional power loss compared to a slick tire.
A factor I don't think you have taken into account that gravel tires are typically wider than road tires and run at a lower pressure, which leads to higher rolling resistance.
I can't point to formal research but the Global Cycling Network YouTube channel has some some tests. 
                
            
They ran with a power meter, on rollers:

28mm GP 5000,   90 PSI,   45 KPH   299W
28mm GP 5000,   70 PSI,   45 KPH   327W
40mm Terra Speed 70 PSI   45 KPH   449W
40mm Terra Speed 40 PSI   45 KPH   516W

The deltas were significant.