Can stress be detected by an fMRI? How does stress damage the brain (if at all)? Is it akin to taking drugs, heavy drinking, or a minor stroke? 

Would an fMRI of a stressed person present evidence of stress?
There is little evidence that stress affects structural MRI (reduction in the volume of the hippocampus). The review article (Effects of stress throughout the lifespan on the brain, behaviour and cognition Lupien et al., 2009) synthesizes the current knowledge in the field. Another article might be of interest (MRI measurement of hippocampal volume in post-traumatic stress disorder: A meta-analysis). 

If you are interested in functional MRI and day-to-day stress, even less is known. The study  (Perfusion functional MRI reveals cerebral blood flow pattern under psychological stress) shows that ventral RPFC (right prefrontal cortex) activation is specifically associated with psychological stress, and this activity persists even beyond the stress-task period.