Doubt it. Might be something weird going on with EMI shielding and hence using the adapter cures the "rolling lines" problem, but I think the two RAMDAC/filter stages are identical (on R300-based boards anyway). Theoretically output quality should be the same on both heads.
Theoretically - it could, but only if you are some CRT quality freak or have crappy vid card, cable or connectors. Preferably that adapter should be built in into the monitor (integrated with it's board). I wonder if that could beat that bunch-o-BNC's approach...
There were some "digital" CRTs which have direct DVI connection, i.e. they have DAC inside them. These CRTs have good display quality regardless the RAMDAC quality of your cards. Unfortunately these CRTs are not produced anymore.