Yes, and this is widely used in forensics just for traces of DNA also on quite old samples.The theoretical limit is just one molecule containing a given nucleotide sequence. For the practical limit somebody more up-to-date than me will no doubt come and tell you.
Often the practical problem will come not from the limitation of sensitivity, but from the very great sensitivity itself! Almost too much can be detected. A given DNA sequence will often be just one amidst dozens or hundreds of others in a sample. In the case of criminal forensics you can pick up an extremely tiny amount of DNA and establish that it almost certainly came from a certain person. But how did that tiny amount get to a crime scene? Might be all sorts of indirect and innocent ways. So you get into forensic dispute. For some more information you could google ‘Low copy number DNA’.
Big subject, interesting, somewhat complicated, implications have been and probably still are controversial. (Also because whenever you mention DNA or genetics many people just go bonkers.)