None that I know of. Yet, I imagine there are huge vacancies within. Exploring it would require a high powered remote with a camera, initially.
Perhaps the water blocked entry disqualifies it as a cave? Not sure.
There are some other springs in that area that are navigable, and have been explored two miles in. Cave spring, on the upper Current River can be entered by canoe. Some fascinating geology in that area. Also quite beautiful. I highly recommend a canoe float, during the off-season.
The Suwanee River in Northern Florida also has some amazing springs, fairly accessible by water, as do some of its tributaries. However, the main river is tannic water. The springs are generally stunningly clear.
Yet I digress in the search for the oldest continual flow of fresh water on the planet. I've googled the query quite a bit, with no answers. Although, there are claims for the oldest continuingly flowing Rivers; one is the New River, in West Virginia. Some irony there.
There are some good you-tubes of cave dives, including some rescues. Indeed, it is a creepy way to die. Peacock Springs, on the Suwanee system has claimed many lives of experienced divers. Usually from silt getting stirred up and visibility lost.
