That bit of "folk wisdom" appears to have originated when the old gas refrigerators were more common, and it still persists among the camp crowd where propane refrigerators are the rule. There's no rational rationale for doing it in a compressor driven refrigerator. Even if you did get some "lumps" of refrigerant in the wrong place(s) the compressor can drive enough gas through the circuit to restore proper distribution, with the only requirement being that there is enough refrigerant to be pumped around.
In a "gas refrigerator" much of the fluid circulation is by convection only, and the most common failure is due to operating at an odd "off level" condition so that the fluid doesn't drip back to the boiler (where the flame heats it). Since the 'fridge fails because the fluid isn't where it's supposed to be, people have the notion that if you move the fluid around all will be well again.
Unfortunately, 'tain't so.
Although the failure happens because the fluid isn't where it needs to be, the way the 'fridge fails is that with the boiler "dry" the anti-corrosion additive (sodium chromate) that keeps the 350 psi 150 F ammonia from eating holes in the plumbing forms a solid cake in the boiler and plugs it up. Once it hardens, the sludge cannot be dissolved back into solution with the actual refrigerant no matter how much you move the refrigerant (ammonia) around.