Even if you probably can't evacuate big hard stones this way, you can certainly evacuate a lot of sludge and soft stones (which are not really stones but rather agglomerations which are not hardened/calcified) and then this can help the bile to flow well, and then this may help to dissolve the hard stones, or at least to improve the flow of bile and consequently the elimination by the liver and the digestion.
There probably won't be any peer reviewed experiment which is not biased if there is nothing to gain by the people doing that.
But you can certainly do an experiment in a scientific way at home and observe the results.
If you wait for the "scientists elites" to determine what is true or false, and if you think they do what they do only to determine what is true or false (and not for money and power), you need to wake up and start to consider it.
The scientific mindset and the scientific method recognizes no authority, only what is objectively observable and measurable and reproducible by others.