You bet it can but it is all going to depend on a number of things:
the thickness of the wall
the height of the wall
the way it is built (new/old bricks, frogs up or down)
the exposure to driving winds
the length of the storm exposure time.

Nearly all the Victorian terraced houses in the UK have solid walls and were built using lime mortar.
 
I rest my case.

My question is quite similar to the original question. Mine a new house, plastered with normal cement and waterproofer mixed through, wall is full two-storey house height (whatever it is), very exposed to a southwesterly wind / rain. cavity filled with the Beads, cavity about 100mm thick, but dampness running down internal surface of outside block and some also on cavity side of internal block. It had been running down to my inside layer to DPC , and then seepeing into internal floor. Removed block at bottom to observe this. On the outside of this wall, my conservatory sits, thus forcing the wind and rain into a corner.

So rain is saturating the outside wall and finding its way down the cavity and showing up inside the house on the ground floor inside where the conservatory is?
 
Are the outside walls rendered block?
 
Has the conservatory got a shallow slope, valley or lead flashing?

Water is showing up inside the house (on the main block of the house),
The outside walls are concrete block.
The conservatory has a slated roof, roughly 45 degrees, lead flashing between conservatory and house. I will attach a picture later, when I get home from work.

The dampness is on the inside cavity on the attached ppicture at location of red circle.

I would have a very good look at the lowest end of the roof cover flashing, I suspect that it is directing some water into the blockwork and it would be better directed 100% into the gutter.
 
Next is window head on the rendered wall and then any plumbing in the room, wall or room above.