'DENNIS THE MENACE'
Wow! Look at all those muscles!
Yeah! He looks like Tarzan!
Tarzan does exist in Earth Prime-Time, but unlike his incarnations in BookWorld and in the Wold Newton Universe, no connection was ever made to the legacy of the Greystoke peerage. Nor to any of the details to be found in the works of Edgar Rice Burroughs. The 'Tarzan' TV series merely took the basics of the iconic figure and updated him to modern times (which in this case was the mid-1960s.)
Toobworld Central isn't closing the door on the legend with just that, however. There's always the possibility - especially now that the original concept has celebrated its 100th anniversary* - that there will one day be a television production about the Lord of the Jungle that adheres to the original vision of Tarzan.
If so, I'm willing to suggest that the Ron Ely portrayal of Tarzan was a grandson to that original John Clayton, Lord Greystoke and the son of Korak. (If he is to be considered Jackie Clayton, I think his portrayal in the TV series runs counter to that found in the Wold Newton Universe.)
Tommy Anderson knows about Tarzan, not from the TV show, but from the ERB books which were slightly fictionalized in order to protect the truth about the Ape Lord. The long line of movies about Tarzan would also be movies in Toobworld and so Tommy probably saw those as well. These presentations could be the work of that shadowy organization I have nicknamed "UNreel", which creates movies and TV shows to serve as a smoke-screen to hide the real lives of certain individuals (like James Bond, the men from U.N.C.L.E., and a Time Lord named the Doctor).
The books and the movies would lend credence to the theory that there was another Tarzan from the earlier part of the Twentieth Century from whom the 1960s Tarzan was descended. (Now all we need is that TV movie or series to support the claim!)
For more about Tarzan's presence in the Wold Newton Universe, check out the site which you'll find linked to in the left. Win Scott Eckert has done a marvelous job in carrying on the work of Philip Jose Farmer with the expansion of the WNU.
* In magazine form; the book publication was in 1914, so there's another chance to celebrate next year!