Should 'stacked' stone have mortar applied in between the stones that have been glued to the surfaces?

A mortar joint is not necessarily required on a stone veneer when a dry stacked look is desired. But, it is very important that the building is properly flashed when using engineered stone of any kind. We see numerous examples of water intrusion on modern homes (3 to 5 years old) where water accumulates on the stone ledge, migrates through the vapor barrier, and rots the wall behind.
This problem is not as prevalent where natural stone is installed with a conventional air space, flashing, and a full mortar joint.
The key answer to your question is that any “engineered” product must be used or installed in strict compliance with the engineer’s spec. The manufacturer would be happy to sell their product for use in as many circumstances as possible- if they don’t recommend it, don’t be surprised when it doesn’t work out as desired.

There are considerations that must be addressed when installing MSV (masonry stone veneer) in a dry stack mode. Dry Stack installations are subject to de-bonding problems when the installer does not fully understand his actions and decisions when installing. Grouted installs do not experience de-bond failures because of three main reasons:
1.The installer is not motivated to adopt a shortcut process which leads to failure in two modes.
2.The grout serves as an additional bonding area which also tends to lock the stone in place.
3.The grout serves as a secondary barrier to water infiltration to the stone back.