YES. It can "Laminarize" the flow. And this will reduce the friction too.
If I think adding infinite number of infinitely thin dividers, we are then actually reinforcing the fluid like concrete is reinforced with steel.
In praxis we are actually just changing the viscosity of the fluid, which -obviously- makes it less turbulent. Study hydraulic fluids/oils; Their main character is the constant visocosity over a wide range. Possibly low, that there is least viscous losses, but enough high that there is no foaming tendency.
It should be noted that the Laminar flow conditions can be hold up to Re > 150 000, and there actually isn't any upper limit for Laminar flow. (ie.. Ven Te Chow, Open Channel Hydraulics)
I think that if you can Increase viscosity, and decrease surface tension, you can reach this kind of flow state really easily. There is a good old video about the issue here;
https://www.youtube.com/watch?v=1_oyqLOqwnI&list=PL0EC6527BE871ABA3&index=12
They say there the same; over Re> 100 000 laminar flow is possible. (~8 min 25 s)
I actually claim that there is no Causality between velocity and Turbulence. It's just a correlation. And thus Reynolds number is actually quite meaningless. More info about this idea is provided here; https://www.youtube.com/playlist?list=PLgUc9kJnDMMExJivT2dWh9dAjdYYUgOFE
For Newtonian fluids (such as water and air), the viscous stress tensor, $T_{ij}$, is proportional to the rate of deformation tensor, $D_{ij}$:
$$D_{ij} = \frac{1}{2}\left(\frac{\partial v_i}{\partial x_j} + \frac{\partial v_j}{\partial x_i}\right)$$
$$T_{ij} = \lambda\Delta\delta_{ij} + 2\mu D_{ij}$$
where $\Delta \equiv D_{11} + D_{22} + D_{33}$. The Navier-Stokes equation for Newtonian fluids can then be written as:
$$\rho\left(\frac{\partial v_i}{\partial t} + v_j\frac{\partial v_i}{\partial x_j}\right) = -\frac{\partial p}{\partial x_i} + \rho B_i + \frac{\partial T_{ij}}{\partial x_j}$$
The Navier-Stokes equation above governs both laminar and turbulent flow using the same stress tensor. This shows that the definition of shear rate is the same in both laminar and turbulent flows, however, their values will be very different.
For non-Newtonian fluids, the same is true. Instead of the stress tensor defined above, replace it with a non-Newtonian stress tensor. Still the same governing equation applies to laminar and turbulent flows so the definition of shear rate is the same for both regimes.
As you mention, turbulent flow does not have nice, orderly layers. As a result, there can be acute stress localizations.
Best Answer
Velocity;
In the case of pipe flow, the velocity remains constant simply through continuity, and the losses are influencing only to pressure. In the open channel flow the velocity depends on up- and downstream conditions, and can therefore even be higher after the object, but also lower if the object causes a hydraulic jump.
Density;
In the pipe flow the density is influenced only through the thermal expansion caused by the pressure turning to heat. In the open channel flow the density can change quite a lot if air entrainment occurs. The Turbulence has only indirect influence to density.