Just talking out of my head right now. Without human interference (let's add some emphasis: INTERFERENCE), all living things get a period of rest roughly at some point every 24 hours. Some get more, some get less, but it seems to me that all living things, plants and animals, were designed to need periods of rest. Go on - try to force yourself to stay awake for weeks on end. At some point your body will take over and you'll pass out.
Can we survive without rest? For some time, yes. Can we thrive without rest? Not really. Do I have any technical data supporting this idea? No, I just know how I and most humans feel after periods of sleep deprivation. Birds can close their eyes and sleep in spite of the light, though they likely would appreciate if those lights were periodically turned off, too. Plants? Hm. No eyes to close. But while you can't do a direct comparison, it would seem to me that there would be some sort of negative outcome of not allowing them to rest simply because they are living things. I can see this resulting in lower seasonal production or a reduced overall life of the plant. Given the right conditions, some pepper plants will live and produce for more than a decade. It would be interesting to track some plants of one of these kinds to see if a trend can be found for a group not getting any periods of darkness.
Just my two cents.... Best wishes with your research!