Can I use the internal Atmega32u4 clock for USB applications?
Had you checked the data sheet before posting a question, you would see the first page bullet point:


  Crystal-less operation for Low Speed mode


and later detail:


  21.4 Crystal-less Operation
  To reduce external components count and BOM cost, the USB module can be configured to operate in lowspeed mode with internal RC oscillator as input source clock for the PLL. The internal RC oscillator is factory
  calibrated to satisfy the USB low speed frequency accuracy within the 0°C and +40°C temperature range.
  For USB full-speed operation only external crystal oscillator or external source clock can be used.


Since HID devices are typically low-speed, for your requirement you can probably do this and implement a low speed device.

If you want to operate at full speed you need a crystal.  The PLL permits using either an 8 or 16 MHz crystal to operate the MCU and develop the internal clock required for USB.

Note additionally that if you use the internal clock it is unclear if you will be able to program the chip over USB - so be sure to provide a way to access the ISP signals.