> A further claim is that increasing welfare reduces work effort. Is this disputed?
Yes, it's disputed. Assuming that you/the GP are correct, and that data do exist that people on welfare have reduced "work effort" (how is that measured?), increased fertility, and increased drug consumption, then you of all people know that correlation doesn't mean causation. It could be that their increased fertility and/or drug consumption caused them to go on to welfare. Or vice versa.
Either way, it would be very hard to draw any conclusions from such data outside of correlation.
In addition to confounding, you also run into lots of statistical biases in such data. As someone else pointed out, poor people are screened for drugs at much higher rates than non-poor, because the jobs that poor people work in are much more likely to require them. As such, even if such data exists, it would be very suspect.
Furthermore, drug testing the general population, even one that has marginally higher drug use rates (and I've seen no convincing data of this either way) runs into the problem of predictive value and false positives (for the same reason screening the general female population under 40 for breast cancer results in massively high rates of false positives).