Jeferson,
The advantage is the internal control circuitry remains powered allowing it to boost from a lower input voltage. This method is typically only useful when boosting the input or input voltage < output voltage. Most of the time with a boost the VIN pin to the IC is only used for powering internal circuitry and is not needed for power conversion. But it may depend part to part if the VIN pin voltage is used for internal control. I know this can be done with two of the boost converter/controllers I work with, the TPS55340 and TPS43060/1. Instead it will be limited by the current limit and not the voltage supply for the IC. This is because with a lower input voltage more input current is needed so there is a higher peak current on the low side FET.
The disadvantage is the IC will be powered by a higher input voltage. If the IC has an internal LDO for powering internal circuitry there will be more power loss in this to step the voltage down. The internal UVLO of the VIN pin cannot be depending on to shut down the IC. The output voltage will hold it up until the input voltage becomes power limited or current limit is hit.
Like I said it depends on the part if this can be done as some parts may require the input voltage for internal control.
Best Regards,
Anthony