You can write the RetroPie image directly to the drive and boot from it - assuming your PI has USB boot enabled. If USB boot is not enabled, then you'll need a sdcard to run Raspberry Pi OS and enable it from raspi-config.
You might not even have to do that, look up the max current draw of your drive. Mine was only 220mA. If USB protocols are being followed your USB current should be at least 500mA with no changes required.
