The lack of sleep has many negative effects associated with it. Maintained sleep deprivation results in a degraded performance over time (in this case reaction time).
Assuming one needs 8 hours of sleep each night, but during the weekdays he only sleeps 6, is it possible to catch up on those lost hours of sleep during the weekend?
There is evidence that 'recovery sleep' is different from ordinary sleep. Carskadon and Dement (2005) measured a sleep pattern that favors Slow Wave Sleep (SWS) after 38 hours without sleep. Personally I also experience it takes me longer to wake up after being sleep deprived, which makes me believe at least your body is trying to make up for something.
A study by Gumenyuk et. al (2011) concludes:
Reduced time in bed is associated with deficiency of the neuronal process associated with change detection, which may recover after one week of sleep extension, whereas attention-dependent neural processes do not normalize after this period of time in habitually short sleeping individuals and may require longer recovery periods.
It gives an indication recovery of some symptoms is possible, but recovery time is not equal for all symptoms. However, the participants in this study seem to be habitual short sleepers.
A more recent study (2015) by Brice Faraut concludes "[...] data suggests a 30-minute nap can reverse the hormonal impact of a night of poor sleep, [...]".
I am wondering whether it is possible to recover from the lost hours over the week during the weekend entirely. E.g. if you lost 8 hours, by sleeping 8 hours more during the weekend. The notion of sleep dept still seems to be up for debate, but perhaps there is more certainty on short term (1 week) effects?
Carskadon, M. A. and Dement, W. C. (2005). Normal human sleep: an overview, chapter 2, pages 13–23, pp. 13-23 In Principles and Practice of Sleep Medicine Elsevier Saunders, Philadelphia (Free PDF)
Gumenyuk V, Roth T, Korzyukov O, Jefferson C, Bowyer S, Drake CL. (2011) Habitual short sleep impacts frontal switch mechanism in attention to novelty. Sleep. 2011 Dec 1;34(12):1659-70. Napping Reverses the Salivary Interleukin-6 and Urinary Norepinephrine Changes Induced by Sleep Restriction