It's a fascinating topic.
The answer is yes, but not in the way you'd hope. Ewd76 was quite correct when he/she said that ultimately, every living person of European extraction is a descendant of Charlemagne. It's impossible to NOT be descended from him and therefore be related to many other royal families all over Europe.
However, I have found that there are MANY false trails on Ancestry.com. Some people may have made innocent mistakes, but I suspect that many have invented links. Working on my own tree, tracing back through pilgrim settlers in New England, I have found at least 4 false lines that tracked back to fantastical pedigrees.
The problem is, once you go through the line generation for generation, checking against an independent source, you swiftly find that at some point, your ancestor was grafted onto a royal parent.
Why do they do this? I don't know. No life losers, I guess. But they're ruining this site.