The article you link to quotes Debby Herbenick for this statement. There are studies showing the levels of Immunoglobulin A (IgA) are increased after morning exercise and studies that indicate increased levels of IgA correlated with sexual activity.
IgA has been shown to be vital in mucosal immunity.
In general, immunization or infection at mucous membranes resulted in high titer of protective antibodies at the mucosal site with absent or low titers in serum, whereas the reverse occurred with parenteral immunization.
Source: Mucosal Immunology (2008)
Supporting the claim by Debby Herbenick, a study by Carl Charnetski and Francis Brennan showed a positive correlation between higher sexual activity and IgA levels in college students. Noting:
Individuals in the frequent group showed significantly higher levels
of IgA than the other three groups, which were comparable
(source: Psychol Rep. 2004 Jun;94(3 Pt 1):839-44.4)
Finally, there have been studies on the effects on the immune system in the broader category of physical exercise too. The positive effects found from such exercise indicate that the source effect is not purely from sex, but either additive or interactive with the effect from generic physical activity.
Findings indicated that long and intensive exercises weaken the
immune system, while moderate and short drills strengthened this
system.
Source: Asian J Sports Med. Sep 2012; 3(3): 185–192.
Therefore, it seems fair to assume a positive effect on IgA levels from morning sex. Based on the study by Hejazi and Hosseini, I'd advise the 'short drill' version to avoid an inadvertent negative effect stemming from endurance exercise.