No. Many vegans (and vegetarians) aim to minimize unnecessary suffering and believe that eating animals causes unnecessary suffering. A crucial premise of this argument is that animals can suffer pain, discomfort, and possibly even more complex unpleasant thoughts or emotions. What is the evidence for that premise? It's a best explanation (or abductive) argument. We have good reasons, based on a wide range of scientific evidence from psychology and neuroscience, to think that complex nervous systems are required to experience suffering, and the mammals we eat (and probably the birds and perhaps the fish) have nervous systems that support these experiences. Plus the behavior of these animals suggests that they can feel pain and discomfort.
Plants do not have nervous systems (or anything analogous) and they do not show the behavior associated with experiencing pain (or anything else). So, we have no reason to think they suffer while they live or when they are harvested. (Personally, I think humanely raising and killing animals is ethically defensible.)
Ironically, souls might be brought into the discussion to cut in both directions. Someone might argue that animals do not have the ineffable soul or mind required to experience suffering, so it's OK to do what may *seem* to cause them pain. Or someone might argue that, even though they don't have nervous systems, plants have the sort of soul (or being) that allows them to experience suffering.