What is the impact of sertraline on white blood cells?
Short answer
While sertraline may theoretically affect the immune system, there is no evidence, as far as I know, that it negatively impacts immune status.

Background
In the article (Atkin-Smith et al., 2015) sertraline (a.k.a. Zoloft, an antidepressant) is shown to block the formation of ‘beads-on-a-string’ protrusions and apoptotic bodies after from dying white blood cells.

Generally, when cells die physiologically, they do not just disintegrate, they undergo programmed cell death called apoptosis.


Beads-on-a-string from a apoptotic monocyte. Source: (Atkin-Smith et al., 2015).

The authors hypothesize that these beads-on-a-string and apoptotic bodies may boost immune responses by containing antigenic material, or that they may contain a warning signal for other immune cells that a pathogen is on the loose.

These claims, however, are hypotheses. 

There are many reported side effects of sertaline, but immune suppressant effects are not evident. The only side effects reported touching on it are, e.g., a fever and a sore throat. However, such general symptoms can be caused by a variety of causes and were not reported frequently. 

Indeed, in a small study in HIV patients, sertraline showed no adverse effects on the immune system (Rabkin et al., 1994).

References
- Atkin-Smith et a. Nat Comm (2015); 6: 7439
- Rabkin et al. J Clin Psychiatry (1994); 55(10):433-9