Can air in pipes cause a faucet to catastrophically fail?
Air in pipes causes what is called water hammer. With air placed in a controlled position, it can be beneficial, acting like a shock absorber. In random places, it can be bad, rapidly accelerating water mass in an uncontrolled direction until it hits a closure, causing the 'hammer'. It is possible for water hammer to damage plumbing systems, especially if allowed to persist over a period of time. The risk is greater in larger pipes because of the greater mass of water involved. The problem isn't so much increased pressure (which can be briefly much greater than normal), it is fast moving water mass impacting on fixed portions of the plumbing.

In your case, I suspect the faucet was close to failure in any case. Any involvement of water hammer would only be the straw that broke the camel's back, not the root cause of the failure. A healthy faucet should be able to resist water hammer at the levels normally seen in residential plumbing. Your faucet was probably greatly weakened by any combination of age, corrosion, inferior materials, improper service or assembly techniques, etc. I wouldn't say it's a common problem, but I've seen it happen a few times on old, cheap faucets. Commonly, faucets develop unrepairable leaks more than actually blowing apart. Then on investigation of the leak, some major faucet part breaks and it becomes obvious it needs to be replaced.

I'm glad my kitchen faucet fell apart. It was an annoying cheap thing. It's replacement is much nicer :)