There seems to be a lot of confusion, conflicting information and assumptions about this matter, so I'd like to clarify that this question is specifically about the 2009 model of MacBook Air. I am aware that most Macs boot from USB just fine. Internet Recovery was introduced to the Air range in 2010, IIRC.
I used to have the 2009 MBA myself back in the day, and I have a vague memory that booting via USB did not work, and that it was the case with all pre-2010 MacBook Airs. However, these days it is no longer easy to find clear information about the matter, official or otherwise. One extant source is here: https://wiki.debian.org/InstallingDebianOn/Apple/MacBookAir/2-1#Installation_medium
I also remember that the "official story" in case of failed hard drives was to boot from Apple's own external optical drive, the USB SuperDrive. The install DVD was even included in the package, despite the machine not having a drive to read it. I'm wondering how it would be that only that particular device worked; could the conditions it fulfills be faked somehow on a normal USB drive?
My situation is that I have been given the opportunity to acquire a cheap 2009 MBA with a failed hard drive, but I don't have physical access to the machine yet. What I am looking to do is replace the hard drive with an OWC SSD and installing a new system (in this case, Linux) on it. However, obviously I wouldn't want to order the new SSD for such an old machine unless I'm sure I can get it to work.