Do vortex generators increase Re of a wing? Do vortex generators (VGs) increase Re of a wing?

I understand that VGs re-energize the boundary layer on a wing.

I understand it turns laminar flow into attached turbulent flow.
Doesn't that mean the Re increases substantially?

If so, wouldn't that increase it's cl/cd, which means lower drag in the 600-900k Re range?
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.