A placebo gets used to determine the margin of error for a particular test. The drug being tested must show significant improvements over the placebo's measurements in order to prove that it is effective.
If your theoretical Drug A performs worse than the placebo, then the effectiveness that it had should be considered to be within the margin of error, and therefore not better than taking nothing at all.
If the drug can't outperform the placebo, then it doesn't make it better than nothing because you're adding chemistry to your body without any assurance that it's going to actually do anything.
But "the placebo" is not a static thing. If we designed experiments differently, the placebo effect might be able to be reduced (say to 3%), in which case drug A would now beat it.
If your theoretical Drug A performs worse than the placebo, then the effectiveness that it had should be considered to be within the margin of error, and therefore not better than taking nothing at all.