It's the factory atmega bootloader, this was a bare chip from atmega.
OK, then it's atmel's DFU bootloader, and the fuses are probably on their defaults.
Whether the chip will go to bootloader on powerup/reset depends on a couple of fuses and maybe some pin status (reading the datasheet).
BOOTRST fuse: if programmed (=0), then the chip *will* jump to bootloader on every powerup/reset. From the datasheet it looks like chips ship with BOOTRST fuse unprogrammed (=1), so that's not good for you.
HWBE fuse: if programmed (=0), then the chip can be forced to go to bootloader on powerup/reset by taking the HWB pin (PE2) low. Reading the datasheet, this fuse is by default programmed (=0) on 32U4 (potentially good for you), and unprogrammed (=1) on 32U4RC (this would be bad, since there's no way then to force entering bootloader).
So:
If the fuses are both unprogrammed (=1) then there's no way to enter the bootloader by hardware, so either you can do it in firmware, or you'll need an AVR ISP programmer and access to 4 pins of the atmega (reset, miso, mosi, sck).
If BOOTRST=1 and HWB=0, then you'll need access to the PE2 pin of the atmega. Tie this to ground, and either reset or power up the board. It will go to bootloader.
To change the fuses, you need an AVR ISP programmer (an arduino or a teensy can act as one if you have those) and access to reset, mosi, miso, sck pins.
EDIT: some further comments: Once you have an ISP programmer, you can reprogram the whole flash including the bootloader if you want. The keyboards I've seen (e.g. bphiphany's controllers) or teensy have BOOTRST fuse programmed, so that the chip enters the bootloader on every reset/powerup. The bootloaders that are used then check whether is was a reset or powerup, and will jump to the application code if it was a powerup (the behaviour is then than the keyboard will look like a keyboard when plugged in, but will go to bootloader when reset while still powered up).