In general, briefly plugging in a new fridge without allowing it to settle or stabilize for a few hours is unlikely to cause significant damage. Modern refrigerators are designed to handle brief power fluctuations and movements during transportation. However, it's still recommended to follow the manufacturer's guidelines for installation and give the fridge adequate time to settle before regular use.
When a refrigerator is transported upright, it minimizes the chances of any damage to the cooling system. This position helps prevent the compressor oil from flowing into the refrigerant lines, which could potentially cause issues. Therefore, transporting the fridge upright is the correct method.
While plugging in the fridge for a few seconds and then unplugging it should not cause immediate harm, it's best to allow the refrigerator to settle for a minimum of 2-4 hours before plugging it in and using it regularly. This settling time allows the refrigerant and oil to settle back into their proper positions and ensures that the compressor is not strained when it starts up.
If you're concerned about any potential damage, it's always a good idea to consult the manufacturer's guidelines or contact their customer support for specific advice related to your refrigerator model.