Burn bootloader to Arduino Uno using ARM-USB-OCD
Probably, but likely not easily

To program an AVR chip you likely want to use the AVR ISP protocol, which is not JTAG, but like JTAG is a synchronous serial protocol with a clock, a data line in each direction, and one additional control pin compared to the several mode/status pins of JTAG.

According to your link, the ARM-USB-OCD is based on an FT2232C USB interface chip.

avrdude documentation indicates that this is an interface it knows how to use, though it will likely take some study to figure out how.

The final question would be wiring - you'll need to figure out which JTAG-style signal names map to which FTDI functional pins, and how those should best be connected to AVR ISP pins in a way which avrdude can use.  Additionally, you'd have to make sure that any buffering between the FTDI chip and the pins is compatible with your needs, both in terms of data direction and voltage level.

Note that you can easily use any ATmega328-based Arduino as an ISP programmer for a same-voltage target - not really production worthy, but if you just need to move your project along today it's a handy option.