Yep that's the theory, the annode is sacrificial and eventually it 'disappears'. Even small DC voltages that are developed when two different metals are in close proximity with a conductive liquid between them cause accelerated corrosion. The supplimentary bonding straps that are fitted to geysers should inhibit the corrosion by preventing voltages forming between different areas of the cylinder if they're fitted correctly but it doesn't prevent corrosion entirely.

Going back to one of your earlier posts I'm interested to know how a geyser cylinder is constructed and whether it is coated with a resin type protection or whether it's galvanised. I'm sure there must be some sort of inner lining to stop the steel cylinder rusting. I'd be interested to see a post mortem on a failed cylinder.