Do people today with a disease caused by single gene mutation that is inheritable - all share a common ancestor?
That can happen, but it's more likely that the disease will be present in more than one family. Diseases with a single, small genetic cause will be more likely to flare up elsewhere (assuming the disease isn't too bad, and it wouldn't be if it's been in the family for 500 years).

However, what you will find is that in your family that disease is almost always present together with some other inherited genetic feature that is nearby on the genome (i.e. an inherited haplotype block). This association is less likely to be shared with other families.