In some cases, yes. USB peripherals that only require low power (i.e. keyboards & mice) can be used without a power adapter. Power in this case is drawn from the host’s USB port.

When high-power USB peripherals are used, a power supply for the USB hub may be required. In other cases, the USB peripheral may require their own power adapters, in this case, a power supply for the hub may not be required. Without ample power though, the USB hub or connected peripherals may not operate correctly. It is recommended to use an included power supply when possible.