Perhaps, but probably not anywhere on Earth.
In order to determine whether or not a plant could truly become sentient, we must first examine sentience within the human brain, according to the Triune model. This will involve breaking the brain into the parts:
- The reptilian complex
- The paleomammalian complex
- The neomammalian complex
The reptilian complex
Consists of the brain stem and the base of the brain. It serves to carry out all of the brain's instinctual and system-sustenance functions.
As far as emulation goes, this complex is relatively simple. Much of its job can be replicated by either an advanced, localized chemical-messaging system, or even by a decentralized neural network.
Evolving such a complex isn't too unfeasible either. Many plants, such as the Venus fly trap, have already developed primitive versions of these systems. A plant would be most likely to evolve in this fashion if it had a set of one or more tasks (like closing a trap around a fly) which required the analysis of one or more input factors in order to produce one or more output factors.
The paleomammalian complex
Consists of the limbic system nodes housed mostly within the interior of the brain. This section is responsible for emotion and internal motivation relative to behaviors such as feeding, mating, and parenting.
Emulating this section would get a little tricky, and would require the development of a central nervous system and a brain, though the brain itself would probably be about half the size of that of a mouse.
As for evolution, this complex would require a rather unique environment, in which traditional methods of mating (pollination) and/or obtaining resources (photosynthesis) are possible and yet not ideal for survival and continuation of the species. An example of this could be an area frequently shrouded by large, dense, slow-moving clouds, or where there is virtually no wind or pollinating insects present.
The neomammalian complex
Consists of the cerebral neocortex, and is the part of the brain responsible for complex thought including social interaction, language, and modeling of future events.
Emulation of this portion of the brain cannot realistically be achieved without a centralized nervous system. At this point, the brain is at least 50% the size of that of a human brain. In addition, the overall sensory and motor/chemical input and output neural nodes within the plant would have to increase substantially.
In order to evolve such a system, the plants would have to be forced by their environment to perform tasks together, like hunting, gathering, and/or competition over territory, in which communication can be extremely advantageous. If this were the case, there would need to be many of them, likely living in small tribes, in close proximity to each other. They would also need to possess resources, such as water, air (carbon dioxide), and/or sunlight, which would be obtained in a collective effort, and would have to be managed by each tribe as a whole.
In order for a biological species to develop intelligence, that species must first be presented with an environment that mandates its development of an intelligence model in order for it to survive. Since the survival tactic utilized by plants relies only on the availability of light, water, and carbon dioxide, as well as a gust of wind or two to carry pollen from one plant to another, it would take a rather unique environment to trigger such a deep-rooted (ha ha) developmental process.