It's theoretically possible to send IR but not with these components. You'd need an IR emitter rather than an IR receiver, and some additional circuitry to turn the iPhone's headphone output into a digital signal that could drive the emitter. (How much extra circuitry depends on what sort of signal the emitter requires and what IR patterns you want to produce.)

We didn't pursue any emitter circuit designs for the book, but it's an intriguing idea.