I don't know if laser engraving or etching could be done -- but I doubt it wouldn't be any easier than engraving.
One of the issues is that the script requires an indentation that is ideally in the underlying metal and then gets covered by copper and chrome. This is a VERY delicate process which caused problems, too. Copper is incredibly soft! If you look at the copper-covered ring shown above, you'll see rubbing marks from shipping and handling above the "o" of Carello -- which had to be polished out before chroming. Then, there were tiny burrs from engraving that also had to be polished away, but that led to issues with polishing compound sticking in the engraved script -- and, so I was told, the more the part is being handled, the worse it gets.
Other than complaining about the scripts looking crooked (which all parties thought was a reasonable concern), I had no direct involvement with engraving and/or chroming. I know one of the rings had to be brought back to metal, straightened, re-coppered, etc before the engraving could be done again. Not that the engraver did anything wrong -- it was just part of the learning curve. The process involved 3 companies in 3 towns in 2 Provinces, Shipping back and forth took about a week in each direction for for each step. At the end of the day, I believe none of the companies made any money on this order (and they probably will not want to go through such pain again).