At this point, I would say no. There are genetic disorders that we know are issues, like BRAC1's link to breast cancer. Other genes we know have some correlation to depression, bipolar, schizophrenia and creativity. And you can have the gene and not have mental illness. We don't want whole genetic testing and labeling people a la the movie "Gattaca".
I do not have a problem with the newborn genetic testing mandated by my state to screen for disorders that pose a threat to the health of the child if not diagnosed early like PKU. It is both limited in scope and clear in the benefit - in many cases preventing disability or severe developmental problems for the child.