Do vortex generators increase Re of a wing?
Reynolds number depends on the free-stream speed, the chord length, fluid density and viscosity. So vortex generator does not modify the Reynolds number. However, it trips the flow aft of the device into turbulent flow. Turbulent flow, in fact, has higher drag than a laminar flow (at the same Re). Therefore, on top of the additional skin friction drag introduced by the VGs, the aerodynamic surface would also have higher drag.