I am not 100% confident in my knowledge of standard garage door opening technology, but I think it would take a substantial amount of hacking your phone to persuade it to transmit and receive radio frequencies in the range of the garage door opening devices. I forget which "ABC" agency is in charge of such things, but they issue very strict requirements for device manufacturers that limit which frequency ranges they may and may not produce. Ultimately these are policies that both insure security for government channels, and regulate broadcast frequencies to provide better quality communication. Imagine if for instance your garage door opened on an FM frequency, then one da it may start opening randomly when I new radio station in town begins broadcasting close to or at its frequency. Likewise imagine your phone had the ability to broadcast in a range similar to an FM range, you may constantly experience "noise" when listening to the radio if someone calls you and the communication is sent via a close frequency. Now these are very over simplified scenarios but possible, and are the reasons the frequency ranges are regulated. So in short, its most likely possible that our phones were engineered purposely in a manner that they just simply can not broadcast atwith frequencies that they are not legally allowed to.
That being said, there is no reason why one couldn't create an external device that say plugs into say the headphone jack and converts an analog audio signal to say a radio signal in the 200-400MHz range or whatever range would be required. However like one poster mentioned, new garage door opening devices use a rolling signal protocol. From the minor amount of research I've done on thi subject, what this means is that your opener does not broadcast he same signal everytime. When the button is pressed and the signal received by the opening motor control unit, the CU shifts "codes" along a specific proprietary developed table and the opener remote is sent a signal to shift as well.
Mind you, this is all a presumption from the limited research I've done.
One would not only need to develop the app to run the peripheral device, but also the device. Likewise thi developer must include all manufacturers code tables and the protocols they use to "shift". That data would be very difficult to come by as its sort of a trade secret so to speak, and if it were publicly available, the security of their systems would be seriously compromised.
Now, I would ask myself why would someone want such technological capabilities? As one poster put it, why fumble with pulling your phone out and unlocking it to open your door while driving? Although it may be helpful for say a latch-key-kid, I think the real advantage is for people who think like me and desire devious ways of utilizing high technology. I.E. having the ability to open garage doors attached to houses that are not my own. Imagine if this app were capable of running down lists of "codes" and blamo! Your neighbors garage door opens, or that random guys garage opens, or the schoolyard bullys door opens and you jack his bike, or short on cash? Take a late night jaunt around the neighborhood opening garage doors and steaing tools, cars, bikes, etc.