There have been several studies that show links between binge drinking and depressive symptoms.
However, it's hard to make any strong statement about a particular level of drinking, because drinking behaviors are so variable, and also to quantify the "level" of the effect on depression, because depression symptoms are also variable.
Finally, it's hard to make causal statements because alcohol use could be a coping mechanism for depressive symptoms rather than causal: many studies approach the relationship from the opposite direction, implying the depressive symptoms are causal for alcohol use.
I've pulled a few papers and can discuss them briefly, though this is not a comprehensive review.
Paljärvi, T., Koskenvuo, M., Poikolainen, K., Kauhanen, J., Sillanmäki, L., & Mäkelä, P. (2009). Binge drinking and depressive symptoms: a 5‐year population‐based cohort study. Addiction, 104(7), 1168-1178.
"This study found a positive association between baseline binge drinking and depressive symptoms 5 years later." "Binge drinking was related to symptoms of depression independently of average intake."
I'd note that this study shows some truly massive relationships, odds ratios of 4-9 for some subcategories; it also seems to have some potential for demonstrating a causal role when they are comparing time 1 drinking to time 2 depression, though still not conclusive.
I think this study gets closest to testing what your question is asking, because it explicitly includes measures of hangovers/binging that are missing from some other studies. It also shows a dose-dependent relationship where more frequent binge drinking is associated with more depressive symptoms, but the relationship is still present even at lower levels of binge drinking compared to non-binge drinking.
Grant, B. F., & Harford, T. C. (1995). Comorbidity between DSM-IV alcohol use disorders and major depression: results of a national survey. Drug and alcohol dependence, 39(3), 197-206.
"Virtually all odds ratios were significantly greater than 1.0, demonstrating that comorbidity of alcohol use disorders and major depression is pervasive in the general population. The magnitude of the association remained stable across the three time frames but diagnostic and subgroup variations in comorbidity were noted. The association between alcohol dependence and major depression was greater than the association between abuse and major depression and the association between alcohol abuse and major depression was consistently greater for females and blacks, compared to their male and non-black counterparts."
This studied focused on older adults, age 57+.
Hill, K. G., White, H. R., Chung, I. J., Hawkins, J. D., & Catalano, R. F. (2000). Early adult outcomes of adolescent binge drinking: person‐and variable‐centered analyses of binge drinking trajectories. Alcoholism: Clinical and Experimental Research, 24(6), 892-901.
"Adolescent alcohol use did not predict educational attain-ment, crime, family roles, or depression."
This study patterned adolescent (<18yo) drinking behaviors into several categories and showed relationships between alcohol use and several other outcomes, but not depression, at age 21.
Okoro, C. A., Brewer, R. D., Naimi, T. S., Moriarty, D. G., Giles, W. H., & Mokdad, A. H. (2004). Binge drinking and health-related quality of life: do popular perceptions match reality?. American journal of preventive medicine, 26(3), 230-233.
"After adjusting for confounding factors, frequent binge drinkers were more likely than non-binge drinkers to experience ≥14 unhealthy days (physical or mental) in the past month (adjusted odds ratio [AOR]=1.39, 95% confidence interval [CI]=1.24–1.56), primarily because they had more mentally unhealthy days than non-binge drinkers (AOR=1.52, 95% CI=1.32–1.75)."
This study combines depressive symptoms with other categories of mental/physical health to assay general quality of life.
And finally I'll end with one meta-analysis:
Boden, J. M., & Fergusson, D. M. (2011). Alcohol and depression. Addiction, 106(5), 906-914.
The current state of the literature suggests a causal linkage between alcohol use disorders and major depression, such that increasing involvement with alcohol increases risk of depression.
They seem to make some arguments for a causal alcohol use -> depression relationship, though I haven't read closely enough to decide whether I am convinced by those arguments.