Let me answer by starting with a question: Plausible in relationship to what?
In the real world we live in, such fantastic mutant powers are simply beyond the realm of human experience simply because most of those powers exceed the realm of physical science as we know them.
Good science fiction (comic fiction) mixes the fantastic with the mundane so being able to say that Wolverine's regeneration as a form of super-stem cell mitosis makes the character appear more plausible but still defies physics and biology as we know it. Such questions as Can Wolverine Survive without oxygen? undermine the scientific validity of said characters but don't make them any less fun or fantastic to consider.
Can Storm's powers be considered plausible in our universe?
Marvel has not been very reliable in explaining the true mechanics of how her powers work. Judging strictly from observation, her powers are a mixture of psionic ability (most likely a form of telekinesis) which Storm has oriented around weather-based phenomena.
We have seen her create micro-climates of blazing heat or freezing cold. Both could be done with a telekinetic molecular control of matter in a specific area.
We have seen her create lightning which could be done by bringing charged particles to her and charging and releasing said particles.
We have seen her gather or create conditions for storms which could be done using telekinesis to alter the relationships of warm and cold air in the atmosphere (baring their existence, she could make the hot or cold air as needed to create the storm conditions she was looking for).
Given such parameters, we would require a person be a powerful telekinetic with the ability to affect a wide range of environmental conditions with precision to create weather-like effects over a vast area.
The pseudoscience around Storm's abilities are no more satisfying than any of the other X-men's so she is in good company.
Is there a set limit on mutant abilities, where they're deemed too unrealistic?
How do the mutant levels correlate with the mutant classifications?