How much power will the MacBook Air output over a single USB port to a non-Apple optical drive?
All I can say is that I bought one of those "sketchy" eBay external Blu-ray drives and it definitely wouldn't work reliably even with power from two USB ports on my machines.
However, I then plugged it in using a single USB port and then for the second USB port I attached it to an Apple 1 Amp USB AC power adapter and it works fine on both my MacBook Pro (2009) and my Windows laptop. It does NOT work fine with a third party 500 mAmp or cheap noname 1 Amp USB adapter. It needs that clean and solid 1 Amp power from the Apple AC adapter.
Note that the Apple external SuperDrive requires more than 2.5 Watts of power (5V 500 mAmp). I suspect it needs about 5 Watts or so (5V 1 Amp), which I believe The MacBook Air can provide, for that drive.