Depression has more than one cause, and "logical emotions" (an interesting way to put it, I assume you meant emotions as in response to external stimuli?) are one of the less common reasons for long-term depression, if I'm not mistaken. Situational-depression is generally just referred to as "the blues" or "being upset about something", and not depression.
There are chemical causes in the brain that have nothing whatever to do with emotions, logic or external stimuli and sociopaths are indeed susceptible to this type of depression.
I am no expert on depression or all expressions of sociopathy, I merely know what I know- but if I am not mistaken, sociopaths have just as much ability to become depressed as anyone else, just not about the same things, certainly not anything related to empathy. Also, your statement negates or forgets the existence of sociopaths with co-morbid disorders.