If a Robot system with an advanced A.I. operating system had the 'ability' to 'do' 'undirected' or 'semi-undirected' introspection and 'form' all sorts of 'thought' structures about any subject matter (that didn't directly have something to do with important 'operating' functions) could these not-necessarily important 'thought structures' and the 'managing' of such cause something analogous to psychological problems in the robot?
Depending on the definition of "psychology" and "psychological problems" sure. The APA defines psychology as "the scientific study of the behavior of individuals and their mental processes." If we take this to only apply to biological systems (as I am sure many researchers do) then no, because the robot is not a biological system and therefore we can not study it under the heading of psychology and we would probably study it under something more akin to "engineering". However, if one is happy applying the same to robots, as I assuming you are, then yes.
Assuming the latter, and if you think that a being's "'ability' to 'do' 'undirected' or 'semi-undirected' introspection and 'form' all sorts of 'thought' structures about any subject matter" is a cause of psychological problems, and we are further assuming that a robot could do this, then yes, the robot will have psychological problems by definition. (Is there direct evidence suggesting these are causes though?)
I guess it happens after creating some robots like baby AI, in this kind of AI, they are trying to create different functional part of brain and by connecting those AI parts to Simulated body sensors.
Those Functional part of Brian could create huge amount of feeling like this thermal Photo which are detected on the AI brain by CPU usage and the Artificial neurons trying to connect to new Brain part as we see it on the Hopfiled networks
IN this Baby AI models, the Main factor of Psychological problem are problem in managing the data and the new connection between the AI brain part, and the limitation of CPU or information which leads to activating some hopfiled models and its create new feature in the Baby AI, that we know as new emotion or feeling, and it could be detected as mental disorder.
Also, I guess, if the Baby AI have had the time or correct information for tracing the brain functional parts and training those weights, it could stable them and this abnormal would reach to new trained weigh and some extra capability.
These features could be seen in some mental disorder that create hallucination and with wrong information could Leeds dangerous situation for patient or its environment, but you can see some features of hopfild models and the brain functional patterns in Livewired book of David eagleman.