No. States that have implemented them have found that they cost more than they save. In many cases they have also been found unconstitutional, and states that implement them are going to find themselves in court spending more money on a case they probably won't win.
Secondly, they don't help anybody. Kicking people off of welfare won't somehow transform them into a non-drug user. If the testing is meant as a way to get people help, that's be one thing, but for the most part they seem to simply be punitive. Removing welfare funding from them doesn't remove them from society, doesn't necessarily remove the burden they place on society, and doesn't alter any of the underlying factors contributing to their situation. So they do nothing but provide symbolic punishment, which I just don't get.