They absolutely did. NKVD executioners drank heavily, and many of those who didn't suffered from extreme distress and mental breakdowns. Nikolai Yezhov, head of the NKVD in 1936-38, was "constantly drunk" and slid ever further into alcoholism and depression as he began to fall out of favor, "boozing at his dacha with his depressed cronies." The situation was so bad that Stalin personally had to comfort and reassure subordinates at times, for example an official investigating the Belorussian Military District who confessed that he "became disorientated" because of the stress. All of this was likely because of the frenzy of the Great Terror under Yezhov, and I understand it got better under Beria, who imposed a more cool and calculated approach.
Source: "Stalin - The Court of the Red Tsar" by Simon Sebag Montefiore
Related ish, anyone mind giving a quick summary of who and what the NKVD was? I never really hear about them.
Does anyone have any recommendations for film or literature that portrays this side of the SS or NKVD?