They should regrow, as long as you are certain you’ve accurately identified the graft union and cut below that (and not, say, the scar from the top of the original scion, which can sometimes also look like a graft union). Avocados aggressively sprout from the root ball when they are cut or frost-killed at ground level.
Yes, I’ve had zero success attempting air layering of avocados. I’ve had better luck with rooting cuttings (though they need to be a different kind of cutting from scionwood, with hardening leaves intact). The etiolation of the lower stem is necessary to initiate roots, but it can be within a tube rather than in a darkroom. So what you’re calling air layering, as long as it’s a light-blocking tube rather than clear plastic or something.
Most of them are not covered by live patents, in the U.S. at least, but some of the new ones might be so that’s definitely something to consider. There may be trademark issues for some that use a trademark name rather than a cultivar name (Dusa is a trademark name, I think, for example). You just have to use the cultivar name instead of the trademark name, for things that are trademarked but no longer patented.