Servo motor analysis
Yes your interpretation is correct. Your model of the servo motor creates a second order differential equation: 
$$I \beta'' + b \beta' + k \beta = \tau_{ext}$$ 

where $\beta$ is the position (in radian angle) , $\tau$ is the externally applied torque (given by the input current and the mechanical load if it exists and is being modeled), $I$ is the moment of inertia of the rotating part, $b$ represents the effect of frictive forces which depend on angular velocity such as your damping friction effect, and $k$ is the effect of position dependent torsional-spring force if it exists. In your system you only consider the angular velocity dependent frictive force and ignore the (non-existing indeed) spring force hence $k=0$. This yields the differential equation

$$I \beta'' + b \beta' = \tau_{ext}$$ 

The system can also be analysed by Laplace transforming the LCCDE, at this point I'm not sure how you reached your $H(s)$, but assuming it's correct then it can be seen that the coefficient $2-100B$ models the frictive force strength and as you have stated; by adjusting $B$ you will adjust the type of solutions from oscillatory underdamped to monotonic overdamped. 

And the physical explanation of the result is also in line with your intuition; with more friction the motor will hardly oscillate but will be slow and inefficient while with less friction the motor will respond faster but will overshoot and osccillate. The critical damping is the optimal solution which reaches the equilibrium as fast fast possible without oscillations. That could be relaxed a little for practical reasons and you can allow some tiny oscillations to improve the dynamic performance considerably, of course provided that a minute amount of overshoot is tolareable.