'Being spared the effects of alcohol' could indicate that Vulcans aren't affected by it. Their blood chemistry being different may mean their bodies don't metabolize alcohol the way humans' do, and so there's no hangover because of the lack of metabolic issues.
Not drinking enough to get hungover/at all technically 'spares' one from a hangover, but that phrasing would be strange and clunky. It'd be like telling someone who just got sunburned at the beach that "I never get sunburned at the beach" to convey that I don't go to the beach, when just saying "I never go to the beach" is a direct statement that logically precludes sunburns from beachgoing.
I think the play is that they're going to spend an episode or two setting up either withdrawal symptoms, or more likely, a resumption of the guilt he felt after the war (casualties he caused as a result of using the super soldier serum. Perhaps he even created/isolated it in the first place and is disheartened by the violence it enables?).
I don't think this episode was meant to explore the trauma, but 'teasing' future plotlines about M'Benga's culpability and/or guilt over the stuff. Remember, Chapel reminds him that he hates it and wonders why he keeps some on him, and he responds that while he does hate it , it might come in handy someday.
I think that serum is what gets him demoted. He and/or Chapel are certainly going to use it again in a situation where he can't just omit it from the after-action report. And if it's S31, then he definitely will get in trouble for holding some.