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
Starting from the conservation of mass:
$$ \dot m_{1}=\dot m_{2} $$
This translates to
$$ \rho_{1} S_{1} V_{1}=\rho_{2} S_{2} V_{2} $$
Assuming incompressible flow, thus $\rho_{1}=\rho_{2}$
gives:
$$S_{1} V_{1}= S_{2} V_{2} $$
With $S_{1} V_{1} = Q_{1}$ , the formula you are using.
This formula follows directly from the mass balance, with only the assumption of incompressible flow. There is no assumption on turbulent or laminar flow, thus this equation holds for both flow types.
With the balance given above you can calculate the speed in at location 2 for the given value of $V_1$ and the ratio of Areas, just as you did. There is no need to account for the flow type.
However, it should be noted here that these are average speeds. If you want to go into further detail, you could include friction forces in the pipe. These friction forces depend on the flow type, and determine the shape in velocity profile, and the resulting velocity.
However, this is significantly more difficult to do than just solving a couple equations.
I know there are some rules of thumb to estimate losses in pipes, but you have to check if their assumptions are valid for your case.
Perhaps you can have a look at Pipe Flow Fluid Mechanics Course
Best Answer
The drag equation can be used to calculate drag force for both laminar and turbulent flow, if we allow $C$ to vary with velocity in a convenient way. This reinterpretation of the equation and meaning of $C$ is sometimes done in practice, especially if one is measuring the drag and expressing the results of measurements as function $C(v)$. This just a practical matter which is useful in the turbulent regime - physically there is no good reason to use single formula for all regimes.
If we don't allow $C$ to vary with velocity and fix it to a single number, the equation can give drag force accurately only in the turbulent regime, and only for limited range of velocities. When studying wide range of velocities, it is not that accurate. The drag force function of velocity is not exactly a single power. That is why function $C(v)$ is introduced, so that the drag equation can be accurate for a wide range of velocities.
For laminar flow, the expression with constant $C$ is completely wrong and should not be used. The accurate expression is closer to linear function:
$$ F = -kv. $$ (In fact the drag force depends also on the acceleration of the body, but this can be handled by redefining the mass of the body).
In common conditions in air, the drag force is linear function of velocity only if the Reynolds number Re is much less than 1. Stuff like microscopic water droplets in fog falling down. Things like falling rocks or flying planes in Earth's atmosphere have turbulent flow. The velocity and the body is just too big to allow for laminar flow.