Yes, moisture rises (and moves horizontally) by capillary action, which depends on the spacing and size of pores within the mortar and brick or block. The denser the brick, or the fewer the voids or pores in the mortar then the less chance of moisture moving far via capillary action. But unless the material is truly waterproof - eg a plastic DPC, then there will always be some movement of water.
I've seen it countless times. Whether this is the problem here is another matter.
To quote from BRE 466 - Understanding Dampness - "Water moves into or through a wall under the action of several forces including capillary action, diffusion, wind, gravity and sorption."