No. It over simplifies what is happening to the point of drawing false correlations. Low serotonin production is strongly linked with low dopamine production but the reverse is less clear. More direct to this conversation sugar and caffeine consumption addresses low dopamine directly, but this coping behavior seeks to address the results of low serotonin, not dopamine. People with low dopamine but regular serotonin also benefit equally from high sugar and caffeine intake, but are substantially less prone to seek sugar and caffeine for that purpose. In the end its about correcting for mood stimulus not task reward stimulus.
Oh I mean that makes perfect sense. You're agreeing with me. Caffeine and sugar give you dopamine. Of course those with low serotonin are likely to have low dopamine - being depressed makes you not want to do stuff. And I can also understand why being depressed would make you want comfort consumables more than being only low dopamine.
As with many behavior impairing/enhancing substances, there are effects on multiple neurotransmitters:
>Caffeine activates noradrenaline neurons and seems to affect the local release of dopamine. Many of the alerting effects of caffeine may be related to the action of the methylxanthine on serotonin neurons. [1]
Or take alcohol, which people typically associate only with GABA:
>Among the neurotransmitter systems linked to the reinforcing effects of alcohol are dopamine, endogenous opiates (i.e., morphinelike neurotransmitters), GABA, serotonin, and glutamate acting at the NMDA receptor (Koob 1996).
Two other things, first the notion that depression can be reduced down to a deficiency of neurotransmitters is almost certainly an oversimplification (if not outright incorrect). What we have is correlation, not causation, where GABA, stress hormones, and other mechanisms also show up. Second, even if this characterization of "low on neurotransmitters => depression" is correct, it is not and has never been just about serotonin:
>The monoamine-deficiency theory posits that the underlying pathophysiological basis of depression is a depletion of the neurotransmitters serotonin, norepinephrine or dopamine in the central nervous system. [2]
