Programming an ATmega32u4 through USB
No - take a look at page 3 of this PDF. All entry to the DFU bootloader is done via reset (which you can't access) or a jump from user code (which you don't have on there because it's a blank IC).

However, how are you intending to configure the device in the first place? You'll want to set your fuses correctly, right, which means access to the ICSP pins, which means access to the reset pin...

But in short, without access to the reset pin this is a no-go.