Hypothetically, turning on the washing machine without detergent after finishing washing your clothes is not the same as doing another rinse cycle, though it might lead to a similar outcome depending on the machine's settings and the water used.
When you run the washing machine without detergent, it means there won't be any soap or detergent in the water to break down dirt, stains, and oils on your clothes. As a result, the clothes won't get cleaned during this cycle, and any remaining detergent from the previous wash may not be fully rinsed out.
However, the machine will likely fill with water and agitate the clothes as it typically does during the rinse cycle. So, in a way, it can mimic a rinse cycle, but without detergent, it won't effectively remove any residual soap or grime from the clothes. This could lead to clothes that feel less fresh or have some detergent residue left on them.
If your intention is to do an additional rinse cycle to ensure your clothes are thoroughly rinsed and free of any detergent residue, it's better to add detergent and run a regular rinse cycle. This way, you'll get the desired result of clean and well-rinsed clothes.