What will happen if one keeps the photosynthesis plant active 24x7?
Ideal conditions for photosynthesis
You mention ideal conditions to carry out photosynthesis, I would just like to point out that this includes carbondioxide levels, temperature, and nutrients as well as light.
Flowering
As anongoodnurse mentions performance might be measured by blooming which, in most flowering plants, has a day-light related component. However, for general growth increasing daylight over the 'natural' day length can often increase yield.
Daylight Cycles
The important point to note is that plants do 'ramp up' at dawn getting ready to start photosynthesizing (for some plants with temporal photosynthesis mechanisms (see CAM photosynthesis) this can be even more important). The reason plants do this is because plants can suffer from 'photobleaching' which can be considered similar to sunburn in humans, if they are not ready for sunlight. Getting 'ready' can involve lots of things including opening stomata (pores) to let CO2 in, changing which metabolic pathways are active,  and moving about chloroplasts inside cells. Plants 'figure out' how and when to ramp up based on circadian rhythms which work well on 24 hour clocks and slight changes over time. Thus 12 hrs to 16 hrs can be a big change, particularly if the change happens by lights coming on earlier. Additionally, the 24 hour 'clock' means that plants will do better with 18hr light then 6hrs dark cycles than 36hrs light 6 hrs dark, because the total cycle length should be about 24hrs.
Photosynthesis Side Effects
Finally, constant photosynthesis does take its toll on plants as photorespiration accompanies photosynthesis. In C3 plants (most crops) this can reduce photosynthetic output by 25% whilst creating ammonia as a byproduct. The ammonia needs to be detoxified as a build up in the cell can cause cell death. Thus plants need enough 'respite' from photosynthesis to deal with photorespiration byproducts or they will suffer.