It can, but only if it's chronic jet-lag (i.e. You're a long haul flight attendant or pilot, or you make long haul trips regularly).
A paper in Nature Neuroscience, Chronic 'jet lag' produces temporal lobe atrophy and spatial cognitive deficits, came to the following conclusion:
Time-zone travelers encounter a pattern of light and darkness, and their endogenous circadian rhythms adapt to the new external time cue until both timing systems synchronize, but the long-term repeated disturbance of synchronization between the two timing systems impairs physiological and psychological health and induces stress. Salivary cortisol levels in cabin crew after repeated exposure to jet lag were significantly higher than after short distance flights, and the higher cortisol levels were associated with cognitive deficits that were dependent on non-semantic stimuli. The present study demonstrates that significant prolonged cortisol elevations produce reduced temporal lobe volume and deficits in spatial learning and memory; these cognitive deficits became apparent after five years of exposure to high cortisol levels.
(I would be interested in reading the full paper if anyone has a Nature subscription.)
By the same author, Chronic jet lag produces cognitive deficits (PDF) measured the saliva cortisol levels of airline ground staff and cabin crew and found that they were elevated for long-haul flight crews even before they departed:
In the present study, all the aircrew subjects had at least several
transmeridian flights in the preceding weeks, which may account
for the increased cortisol secretion in the aircrew subjects. This
finding is in contrast to earlier reports of no increased cortisol
secretion after transmeridian flying (Desir et al., 1981). The study
of Desir et al. (1981), however, was conducted in subjects that had
no circadian rhythm disruption in the previous year. International transmeridian flying was associated with significantly raised salivary cortisol compared to short-distance flying in the same cabin crew subjects on the outward journey. This indicates that the increase in circulating cortisol was not caused by the effect of flying per se. It is possible, however, that anticipation of
the deleterious effects of “jet lag” was stressful for these subjects, and this caused the increase in cortisol secretion before the
circadian disruption. This effect was observed across all four
career cohorts, which suggests that it is not something to which
the subjects were able to adapt. One might have expected that
after 4 years of flight experience, the subjects would have adopted
a successful strategy for reducing the negative impact of flying.
Recent evidence has shown that chronic exposure to high levels
of circulating corticosteroids impairs cognitive function in both
animals and humans (Lupien et al., 1994, 1997, 1998; McEwen
and Sapolsky, 1995). After 4 years of transmeridian flying expe-
rience, the aircrew showed statistically significant correct key rate
and reaction time deficits. The delayed onset of this decrement
implies that exposure to the elevated level of cortisol for 4 years
had impaired these functions a result, which is in line with
previous findings (Lupien et al., 1994, 1997; McEwen and Sapol-
sky, 1995). Years of career also appeared to negatively affect the
ground crew’s cognitive performance as well. This decline may be
explained by age-related influences, however, further study is
required to confirm this (Grady et al., 1998; Hazlett et al., 1998).