Yes. The "edges" of the ages as we talk about them in modern times were not stark, but rather transitional. Not everywhere adopted or was exposed to bronze-working technology at the same time in all places, and some societies continued without any significant use of bronze (and all the adjacent technologies) for some centuries after the transition.

These days we tend to use the Chalcolithic or "Eneolithic" or "Copper Age" (the last subdivision of the "Stone Age," which term nobody really uses much anymore) as a catch-all for transitional societies. Though the names focus on tool material type, there were more technologies and tendencies at play besides just metal smelting. In general, the transition from Neolithic to Bronze Age involves increasing urbanization, expanded or intensifying trade ties, a compounding economic complexity, social hierarchical developments, development of writing, changes in burial practice, change or further development in religious practice, changes to agricultural practice (generally swinging more towards sedentary agriculture and husbandry and away from "gathering") and so on. Some areas, due to lack of access to ores, progressed beyond the "Neolithic" in some of these areas but did not develop widespread bronze tool use for some time hence. As with most topics, it is much more messy than we would like as we attempt to categorize and fit things into neat columns.