Effects of selection on effective population size
From Conner and Hartl's A primer of ecological genetics:


  "Any variance in reproductive success among individuals greater than
  random expectations, a commonplace concurrence in natural populations,
  reduces effective population size."


So yes, selection does reduce the effective population size and for the reason you suggest - it removes some individuals from the mating pool/ reduces their contribution to the next generation. Mathematically it can be derived as

$N_e \approx \frac{ 8N_a}{V_m + V_f + 4 }$

where $V_m$ and $V_f$ are sex-specific variances of offspring production (males are often more variable in reproductive success than females). 

They give an example of selection affecting $N_e$, in a population of deer 33 males had four times the variance ($V_m$ = 41.9) in reproductive success of 35 females where variance was $V_f$ = 9.1. Thus effective population size was

$N_e \approx \frac{ 8 * (33 + 35)}{41.9 + 9.1 + 4 } = 9.9$

The notation $N_a$ is the actual number of individuals in the population. This can be seen in the calculation of effective population size when the number of males and females are not equal

$N_e = \frac{4 N_m N_f}{N_m + N_f} = \frac{4 N_m N_f}{N_a}$

An example is a population of 80 males and 80 females compared to a population of 70 males and 90 females. Both populations have equal sizes but effective population size is reduced by unequal sex ratios

$N_e = \frac{4 * 80 * 80}{160} = 160 \neq \frac{4 * 70 * 90}{160} = 157.5$