No matter its type, the CRTC never buffers its counters.
The only value that is saved in a buffer in the CRTC is the video pointer MA because it is reloaded at each raster line start. R12/R13 is loaded only once per frame, in MA and MA', at the first line of the first character of the frame. The counter MA then reload MA' at each raster line start. And at each new character line start, MA' captures the current value of MA.
The exception is the CRTC 1 for which the MA is reloaded at each line start with R12/R13 instead of MA' as long as VCC=0.