Would you still have any trace of DNA from an ancestor from the BC times?

Yes, absolutely. We have DNA from before we were human. Although because we get half our DNA from each of our parents and each half is randomly selected from all of their genes, they get shuffled around each generation, so that over time any given ancestor's genes can completely disappear from the gene pool. So even if your descends continue to make descendants, there is no guarantee that any of your genes will continue to be ped on.