u/itsallfolklore and I both wrote about this here, with my answer focusing more on the textual history and his more on the folkloric aspects. The long and short of it, though, is no. The first textual mentions of Arthur are centuries after he supposedly lived, and our most reliable source for post-Roman Britain (Bede's Ecclesiastical History of the English People) makes no mention of him. It's possible the original folklore was based on a real Celtic warlord, but if so, that person's life almost certainly had minimal resemblance to the modern Arthur.

Furthermore, as I talk about a bit in my old answer, the Arthur narrative changes quite a bit during the Middle Ages. Things like The Round Table, the quests of his knights, Excalibur, the Sword in the Stone and so on are all inventions of the Later Middle Ages. Even Geoffrey of Monmouth's Arthur (our first major textual source) is very different from the Arthur we know today, and that work was finished in 1136, centuries after Arthur supposedly lived.