Exactly as Ryan says above, the onset of photosaturation and photoinhibition (under otherwise normal and constant environmental conditions) depend on light INTENSITY. The light dependent reactions in photosynthesis happen so quickly (fractions of a second) they are effectively instantaneous for our purposes. To attain photosaturation or photoinhibition the parameter of importance is light intensity.
Hence, if the light intensity is subsaturating you could leave the light on 24/7 and you will NEVER attain photosaturation nor photoinhibition. Constant light may screw up other aspects of the organisms' biology, but higher light intensity is required to reach photosaturation or photoinhibition.
At or below saturating light intensity the quantity of net carbon fixation (net primary production) does depend on photoperiod. For instance, if X light intensity is at or below photosaturation then a photosynthetic organism will fix more C in 12 hrs than in 6 hrs. Exactly how much depends on where we are on the P/E curve. The RATE of photosynthesis depends on light intensity, the net total daily carbon fixation (NPP) depends on the 1) the rate of photosynthesis and 2) the photoperiod.
Photoinhibition occurs when the photosynthetic apparatus (collection of a photopigments and a variety of proteins) becomes damaged. Usually this happens through the production of excessive reactive oxygen species, which happens at high light intensity. The more ROS are produced the more photocenters are damaged and the more of them there will be that need replacement/repair. Again, the RATE of photodamage depends on light intensity (all else equal), the net daily amount of photodamage depends on 1) the rate of photodamage and 2) the photoperiod.
It all comes back to where we fall on a P/E curve though. We want light intensity bright enough that we are getting a sufficiently high rate of photosynthesis, but we don't want so much light we are causing photoinhibition (and significant photodamage). If we have enough light, but not too much, we should be able to run a good, long photoperiod, thereby getting lots of carbon fixation and ultimately happy, healthy, fast-growing critters.
cj