Typically, no. For identification comparision purposes, investigators tend to look at
VNTRs, which are very informative from an identification standpoint, but almost meaningless from a medical/privacy standpoint.
Similarly, the "database" that has been collected (
CODIS) keeps track of only 13 genes (plus a fourteenth for sex). I believe there is one suspected linkage between one of those genes and one genetic disease. If all that is stored is the CODIS data, there's not much that someone can learn about your genetics from your CODIS data.
Of course, if the physical DNA is what's stored, then they could always re-analyze the data and learn anything they like. But this would be prohibitively difficult and expensive. I can put the CODIS data for a million people onto a thumb drive; actual DNA samples for a million people would require a large climate controlled building.