From wikipedia: "The flow reversal is primarily caused by an adverse pressure gradient imposed on the boundary layer by the outer potential flow"
From this website http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/introvisc/node9.html: "One of the severe effects of an adverse pressure gradient is to separate the flow."
From Fundamentals of Aerodynamics by John D Anderson Jr., page 795: "Figure 15.3 Separated flow induced by an adverse pressure gradient". Figure 15.3 is very similar to the image on the left side of your post.
If I understand your question correctly, you are asking if separated flow causes low pressure zones, and I believe the answer is technically no. An adverse pressure gradient causes the separated flow, and where we see separated flow there is lower pressure. However, the separation of flow is not the instigator, it is the adverse pressure gradient in viscous fluids due to shear stress and the retarding forces acting on the fluid as it flows past a body that causes the flow separation.
Note that the setting up of an adverse pressure gradient will depend on the geometry of the body that the fluid is flowing over, and at what angle the fluid is flowing over the body. If pressure increases along the body, then I believe, an adverse pressure gradient will be set up.