I thought for sure he had actually killed someone himself, and early on around the Tflis bank robbery period there were times he almost did.
But Simon Sebag Montefiore recently wrote a biography on Stalin's earlier years (Young Stalin, 2007, Vintage Books), and he states a few times that Stalin himself never pulled a trigger during his whole life (that resulted in someone getting killed), he always had someone else do it. There was a military officer assassinated by small grenades (known as "apples") back in the pre-revolution days and he was close enough to get hit with shrapnel pretty seriously, but never threw them himself.
Even when imprisoned, others would beat or threaten for Stalin, he seemed to enjoy being able to ply others to get their fists bloody on his behalf, and seemed to be one of the self-affirmations of his power.
I would expect that he did not purposely witness any executions- his whole persona was that he didn't take responsibility for his ordered actions. He was rarely present during any major power plays during the revolution itself (grabbing money, traveling Europe, or being exiled/imprisoned) and was always known for disappearing when least expected. His biggest enemies were often 'dispatched' while nowhere near him (Trotsky in Mexico, various enemies sent to Siberia and elsewhere).
There isn't (as far as I've seen, fwiw) a single eye-witness claim that he killed anyone himself. People feared him from his childhood up to the day he died, but few ever saw him actually lose his temper, much less actually become physically violent. His normal behavior was to openly brood when 'disappointed', threaten to become violent, and to offer small bits of threats prior to an untimely incident taking place (carried out by a henchman).
His power was cultivated by the company he kept, and it helped keep him from being a solitary target as he moved his way up the political food-chain. If you hated him, you knew you had to deal with a bunch of his supporters, not ever merely himself, and he cultivated that by associating with criminals throughout his life. You had to worry about his friends as much as the man himself.
So it's doubtful that he'd take the time to watch someone die- only if it served a purpose towards the others present at that moment would I surmise that he'd "take the time" to engage in witnessing something like an execution.