Nope. Calcium gives a higher TBN, ash and provides longer OCI, maybe 1-2%, but that's almost nothing.
Ester based oils are known as cleansing. Regular HC oil even with high ppm of Ca and short OCI will not clean, especially one of the hottest zones- pistons and rings.
The best way to cope with dirty piston rings, not even rings, but their channels and special holes at the bottom of these channels is to unassemble your engine and use agressive cleaner. Also you can add such a cleaner through your spark plug holes and leave for some time. After that start your engine without spark plugs several times, but don't forget to put some cloth(rag) over plug holes, otherwise be ready to see how deposit's pieces will shoot your roof.