No, the language is still constructed. The label "constructed language" has to do with how the language was created, not how it is subsequently used. A constructed language is consciously created for an express purpose. It is likely however that should native speakers of a constructed language arise the language would start down the path towards spawning a natural language. Or rather, more likely, several daughter languages which would be considered natural. They would be considered natural because they arose due to the action of natural evolutionary forces on an ancestral language. But all languages start life as dialects, so dialects would have to appear in a constructed language first. As yet, this has never happened and it may be impossible for an unknown reason.