It should be possible. The IR receiver is already a "bitbang" receiver, as it's just a sensor hooked up to a GPIO.
I have a LIRC driver somewhere in my development tree. It created a kernel module that allowed the IR sensor to be used with LIRC. Unfortunately, while I could record data using "mode2", I wasn't ever able to "train" the remote to ever work. The LIRC documentation isn't very good at all for developers who want to add drivers.
A corresponding "transmit" driver should be equally easy (or hard) to write, especially since all the GPIOs are hooked up to the Linux kernel GPIO system.
The one caveat is that the IR extender physically switches off the internal IR sensor. So you can only have one or the other. Still, if you wanted, you could in theory replace the sensor with a LED and create an IR blaster.