Using Arduino as ISP to burn sketch directly to ATmega328 without first installing a bootloader on the ATmega328
It is possible to skip the Burn Bootloader step. When you do Upload Using Programmer the bootloader is overwritten and thus serves no purpose. However, there is another reason for the Burn Bootloader step, to set the correct fuses for your board selection. The fuse settings configure things on the ATmega328 such as clock speed and clock source. If the ATmega328 you are using doesn't happen to have the correct fuse settings for the board selection you're using in the IDE then things may not work or may not work correctly. For this reason it's best to always do the Burn Bootloader step the first time you use the ATmega328 and any time you change the board selection or other settings related to that board selection(such as custom Tools menu settings). Since you're not using an external clock source for your ATmega328 make sure that you don't select a board that is configured for an external clock as this will cause the chip to no longer work until you have connected an external clock.