Yes, and arguably, all concepts are vague insofar as all concepts are described with language, and language wrestles with vagueness.
First, so we're clear, there is a different between a concept and an explanation of a concept. From WP:
Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks underlying principles, thoughts and beliefs. They play an important role in all aspects of cognition.
In this way, concepts resemble emotions in that a description of an emotion ("Happiness is having nothing to worry about and is a feeling of elation") is not the actual emotion itself, but a linguistic artifact which describes the experience. While precising definitions, examples, and explanations can and are used to reduce vagueness, they are by no means perfect solutions, and some have argued that vagueness inheres to reality itself. From WP:
Vagueness is a major topic of research in philosophical logic, where it serves as a potential challenge to classical logic. Work in formal semantics has sought to provide a compositional semantics for vague expressions in natural language. Work in philosophy of language has addressed implications of vagueness for the theory of meaning, while metaphysicians have considered whether reality itself is vague.
So, there is a balance with concepts between precision and vagueness that often requires a normative approach to deciding when a concept is adequately clear, and that might range anywhere from a simple intuitive understanding through a complex definition in a specialty reference all the way to an exegesis on a topic. Philosophers use all three. For instance, discussion about 'consciousness', which is generally taken to be a vague term, might range from an appeal to personal experience, might lead to the description in the article Consciousness in the Stanford Encyclopedia of Philosophy, or may be resolved to satisfaction relying on Daniel Dennett's book on the topic, Consciousness Explained (GB).
Ultimately, what a community of language users finds an acceptable level of disambiguation is matter of discussion, debate, and consent according to the rules of the language game in play. Thus, there is no objective, universal rule of when a concept has been sufficiently disambiguated, and rather depends on the context. A discussion of consciousness in elementary school will be necessarily different from one in a graduate level philosophy class on the topic.