Do I need to clear the bootloader when using Parallel Programmer?

Usually you would use a parallel programmer just to load a fresh bootloader. When you burn a bootloader the chip is completely erased as part of the process.

If you want to get rid of the bootloader to make more space you won't be programming an Arduino anymore and any problems you encounter will be outside the scope of this forum. Perhaps you should visit http://www.AVRFreaks.net/ where the people who do raw AVR programming hang out.